Trentelman, Harry L., Rapisarda, Paolo
In this paper we revisit the problems of passivity and bounded realness preserving model reduction by balanced truncation. In the behavioral framework, these problems can be considered as special...
Lyapunov stability analysis of higher-order 2-D systems (2009)
Kojima, Chiaki, Rapisarda, Paolo, Takaba, Kiyotsugu
We give necessary and sufficient conditions, based on the existence of a Lyapunov functional, for the asymptotic stability of asquareautonomous2-D behavior in the sense of Valcher.
Exact identification of lossless systems (2009)
We illustrate an algorithm to exactly identify a lossless system from a given trajectory. Performing a rank-revealing factorization of a Gramian matrix constructed from the data, a state sequence...
Rapisarda, Paolo, Takaba, Kiyotsugu
We present a counterexample contradicting the equivalence of statements (i)-(ii) and (iii)-(v) of Theorem 1 of Fu, P., Chen, J., and S.I. Niculescu (2006). "Generalized eigenvalue-based stability...
Balanced state-space representations: a polynomial algebraic approach (2009)
Rapisarda, Paolo, Trentelman, Harry L.
We show how to compute a minimal Riccati-balanced state map and a minimal Riccati-balanced state space representation starting from an image representation of a strictly dissipative system. The...
Data-driven simulation and control (2008)
Markovsky, Ivan, Rapisarda, Paolo
Classical linear time-invariant system simulation methods are based on a transfer function, impulse response, or input/state/output representation. We present a method for computing the response of a...
Higher-order linear lossless systems (2008)
Rao, Shodhan, Rapisarda, Paolo
We define a lossless autonomous system as one having a quadratic differential form associated with it called the total energy, which obeys the property of positivity and which is conserved. In this...
Rapisarda, Paolo, Markovsky, Ivan
We study the linear quadratic control problem from a representation-free point of view, and we show that this formulation brings forth two self-contained and original proofs of the optimality of...
Model reduction of dissipative systems by balanced truncation (2008)
Ha, Minh B., Rapisarda, Paolo, Trentelman, Harry L.
Given a dissipative system behavior with general supply rate, say a Sigma-dissipative system, we propose a balanced truncation method to obtain a reduced-order system behavior which is again...
Autonomous linear lossless systems (2008)
Rao, Shodhan, Rapisarda, Paolo
We define a lossless autonomous system as one having a quadratic differential form associated with it called an energy function, which is positive and which is conserved. We define an oscillatory...
On the Takagi interpolation problem (2008)
Dedicated to Professor Paul A. Fuhrmann on the occasion of his retirement.
Computation of LTI system responses directly from input/output data 1 (2007)
Ivan Markovsky, Jan C. Willems, Paolo Rapisarda, Bart L. M, De Moor
Submitted for publication to CDC 2004
Balanced State Representations from Higher Order Differential Equations (2007)
Paolo Rapisarda, Jan C. Willems
We present an algorithm to compute a balanced state representation of a system from its description in terms of polynomial matrices and higher-order differential equations. Keywords: Behaviors, image...
On the state of behaviors (2007)
Fuhrmann, Paul A., Rapisarda, Paolo, Yamamoto, Yutaka
The theme of the present paper is the study of the concept of state and the corresponding state maps in the context of Willems’ behavioral theory. We concentrate on Markovian system and their...
On the Takagi interpolation problem (2007)
Kaneko, Osamu, Rapisarda, Paolo
In this paper we approach the interpolation problem of Takagi from the perspective of time-series modeling. The framework of exact identification and the notion of MPUM are used in order to...
On the state of behaviors (2007)
Fuhrmann, Paul A., Rapisarda, Paolo, Yamamoto, Yutaka
The theme of the present paper is the study of the concept of state and the corresponding state maps in the context of Willems’ behavioral theory. We concentrate on Markovian system and their...
On the Takagi interpolation problem (2007)
Kaneko, Osamu, Rapisarda, Paolo
In this paper we approach the interpolation problem of Takagi from the perspective of time-series modeling. The framework of exact identification and the notion of MPUM are used in order to...
On the optimality of state feedback in linear quadratic control (2007)
Rapisarda, Paolo, Markovsky, Ivan
We study the linear quadratic control problem from a representation-free point of view, and we show that this formulation brings forth several results of independent interest. Among these results are...
On the optimality of state feedback in linear quadratic control (2007)
Rapisarda, Paolo, Markovsky, Ivan
We study the linear quadratic control problem from a representation-free point of view, and we show that this formulation brings forth several results of independent interest. Among these results are...
Model Reduction for Controllable Systems (2007)
Ha, B.M., Rapisarda, Paolo, Trentelman, Harry L.
In the papers [1], [7] a new scheme for passivity-preserving model reduction has been proposed. We have shown in [2] that the approach can also be interpreted from a dissipativity theory point of...
On the linear quadratic data-driven control (2007)
Markovsky, Ivan, Rapisarda, Paolo
The classical approach for solving control problems is model based: first a model representation is derived from given data of the plant and then a control law is synthesized using the model and the...
Model Reduction for Controllable Systems (2007)
Ha, B.M., Rapisarda, Paolo, Trentelman, Harry L.
In the papers [1], [7] a new scheme for passivity-preserving model reduction has been proposed. We have shown in [2] that the approach can also be interpreted from a dissipativity theory point of...
On the linear quadratic data-driven control (2007)
Markovsky, Ivan, Rapisarda, Paolo
The classical approach for solving control problems is model based: first a model representation is derived from given data of the plant and then a control law is synthesized using the model and the...
Data-driven simulation and control (2007)
Markovsky, Ivan, Rapisarda, Paolo
Classical linear time-invariant system simulation methods are based on a transfer function, impulse response, or input/state/output representation. We present a method for computing the response of a...
Kotenkaisekigaku ni okeru hokanmondai to Most Powerful Unfalsified Model (MPUM) (2007)
Kaneko, Osamu, Rapisarda, Paolo
This review article (in Japanese) presents the essentials of exact identification. Particular attention is given to the formalization of interpolation problems involving stability- and metric...
Kotenkaisekigaku ni okeru hokanmondai to Most Powerful Unfalsified Model (MPUM) (2007)
Kaneko, Osamu, Rapisarda, Paolo
This review article (in Japanese) presents the essentials of exact identification. Particular attention is given to the formalization of interpolation problems involving stability- and metric...
Data-driven simulation and control (2007)
Markovsky, Ivan, Rapisarda, Paolo
Classical linear time-invariant system simulation methods are based on a transfer function, impulse response, or input/state/output representation. We present a method for computing the response of a...
Kotenkaisekigaku ni okeru hokanmondai to Most Powerful Unfalsified Model (MPUM) (2007)
Kaneko, Osamu, Rapisarda, Paolo
This review article (in Japanese) presents the essentials of exact identification. Particular attention is given to the formalization of interpolation problems involving stability- and metric...
Canonical forms for polynomial and quadratic differential operators (2007)
Kojima, Chiaki, Rapisarda, Paolo, Takaba, Kiyotsugu
We define the canonical representative for the equivalence class consistingof all polynomial- and quadratic differential operators that take the same values on a given subspaceof C
Canonical forms for polynomial and quadratic differential operators (2007)
Kojima, Chiaki, Rapisarda, Paolo, Takaba, Kiyotsugu
We define the canonical representative for the equivalence class consistingof all polynomial- and quadratic differential operators that take the same values on a given subspaceof C
Canonical forms for polynomial and quadratic differential operators (2007)
Kojima, Chiaki, Rapisarda, Paolo, Takaba, Kiyotsugu
We define the canonical representative for the equivalence class consistingof all polynomial- and quadratic differential operators that take the same values on a given subspaceof C
Canonical forms for polynomial and quadratic differential operators (2007)
Kojima, Chiaki, Rapisarda, Paolo, Takaba, Kiyotsugu
We define the canonical representative for the equivalence class consistingof all polynomial- and quadratic differential operators that take the same values on a given subspaceof C
Canonical forms for polynomial and quadratic differential operators (2007)
Kojima, Chiaki, Rapisarda, Paolo, Takaba, Kiyotsugu
We define the canonical representative for the equivalence class consistingof all polynomial- and quadratic differential operators that take the same values on a given subspaceof C
Higher-order linear lossless systems (2007)
Rao, Shodhan, Rapisarda, Paolo
We define a lossless autonomous system as one having a quadratic differential form associated with it called the total energy, which obeys the property of positivity and which is conserved. In this...
Canonical forms for polynomial and quadratic differential operators (2007)
Kojima, Chiaki, Rapisarda, Paolo, Takaba, Kiyotsugu
We define the canonical representative for the equivalence class consistingof all polynomial- and quadratic differential operators that take the same values on a given subspaceof C
Dissipativity preserving model reduction by retention of tra jectories of minimal dissipation (2007)
Ha, Minh Binh, Rapisarda, Paolo, Trentelman, Harry L.
We present a method for model reduction based on ideas from the behavioral theory of dissipative systems, in which the reduced-order model is required to reproduce a subset of the set of tra...
Dissipativity preserving model reduction by retention of tra jectories of minimal dissipation (2007)
Ha, Minh Binh, Rapisarda, Paolo, Trentelman, Harry L.
We present a method for model reduction based on ideas from the behavioral theory of dissipative systems, in which the reduced-order model is required to reproduce a subset of the set of tra...
Minicourse on behavioral systems theory- Lecture 2: Representations and annihilators of LTIDS (2006)
Minicourse on behavioral systems theory- Lecture 2: Representations and annihilators of LTIDS (2006)
Minicourse on behavioral systems theory- Lecture 4: Bilinear and quadratic differential forms (2006)
Minicourse on behavioral systems theory- Lecture 4: Bilinear and quadratic differential forms (2006)
Kojima, Chiaki, Takaba, Kiyotsugu, Kaneko, Osamu, Rapisarda, Paolo
This paper is concerned with a characterization of all symmetric solutions to the discrete-time algebraic Riccati equation (DARE). Dissipation theory and quadratic difference forms from the...
On the state of behaviors (2006)
Fuhrmann, Paul A., Rapisarda, Paolo, Yamamoto, Yutaka
The theme of the present paper is the study of the concept of state and the corresponding state maps in the context of Willems’ behavioral theory. We concentrate on Markovian system and their...
On the Takagi interpolation problem (2006)
Kaneko, Osamu, Rapisarda, Paolo
In this paper we approach the interpolation problem of Takagi from the perspective of time-series modeling. The framework of exact identification and the notion of MPUM are used in order to...
Kojima, Chiaki, Takaba, Kiyotsugu, Kaneko, Osamu, Rapisarda, Paolo
This paper is concerned with a characterization of all symmetric solutions to the discrete-time algebraic Riccati equation (DARE). Dissipation theory and quadratic difference forms from the...
Kojima, Chiaki, Takaba, Kiyotsugu, Kaneko, Osamu, Rapisarda, Paolo
This paper is concerned with a characterization of all symmetric solutions to the discrete-time algebraic Riccati equation (DARE). Dissipation theory and quadratic difference forms from the...
Bases of conserved and zero-mean quadratic quantities for linear oscillatory systems (2006)
Rao, Shodhan, Rapisarda, Paolo
We study the structure and properties of the set of intrinsically zero-mean quadratic quantities for linear oscillatory systems, i.e. quantities having a zero asymptotic average only on such a...
Bases of conserved and zero-mean quadratic quantities for linear oscillatory systems (2006)
Rao, Shodhan, Rapisarda, Paolo
We study the structure and properties of the set of intrinsically zero-mean quadratic quantities for linear oscillatory systems, i.e. quantities having a zero asymptotic average only on such a...
Solution of polynomial Lyapunov and Sylvester equations (2006)
Peeters, Ralf, Rapisarda, Paolo
A two-variable polynomial approach to solve the one-variable polynomial Lyapunov and Sylvester equations is proposed. Lifting the problem from the one-variable to the two-variable context gives rise...
Solution of polynomial Lyapunov and Sylvester equations (2006)
Peeters, Ralf, Rapisarda, Paolo
A two-variable polynomial approach to solve the one-variable polynomial Lyapunov and Sylvester equations is proposed. Lifting the problem from the one-variable to the two-variable context gives rise...
A behavioral view of Nevanlinna-Pick interpolation (2005)
Pendharkar, Ishan, Pillai, Harish K., Rapisarda, Paolo
The classical Nevanlinna-Pick (NP) interpolation problem is about finding a rational function that satisfies given interpolation conditions, along with a norm condition. In this paper we address the...
Interpolation with bilinear differential forms (2005)
Pendharkar, Ishan, Rapisarda, Paolo, Pillai, Harish K.
We present a recursive algorithm for modeling with bilinear differential forms. We discuss applications of this algorithm for interpolation with symmetric bivariate polynomials, and for computing...
A behavioral view of Nevanlinna-Pick interpolation (2005)
Pendharkar, Ishan, Pillai, Harish K., Rapisarda, Paolo
The classical Nevanlinna-Pick (NP) interpolation problem is about finding a rational function that satisfies given interpolation conditions, along with a norm condition. In this paper we address the...
Interpolation with bilinear differential forms (2005)
Pendharkar, Ishan, Rapisarda, Paolo, Pillai, Harish K.
We present a recursive algorithm for modeling with bilinear differential forms. We discuss applications of this algorithm for interpolation with symmetric bivariate polynomials, and for computing...
Vector-exponential time-series modeling for polynomial J-spectral factorization (2005)
Pendharkar, Ishan, Pillai, Harish K., Rapisarda, Paolo
An iterative algorithm to perform the J-spectral factorization of a para-Hermitian matrix is presented. The algorithm proceeds by computing a special kernel representation of an interpolant for a...
Vector-exponential time-series modeling for polynomial J-spectral factorization (2005)
Pendharkar, Ishan, Pillai, Harish K., Rapisarda, Paolo
An iterative algorithm to perform the J-spectral factorization of a para-Hermitian matrix is presented. The algorithm proceeds by computing a special kernel representation of an interpolant for a...
Totally dissipative systems (2005)
Kaneko, Osamu, Takaba, Kiyotsugu, Rapisarda, Paolo
In a totally dissipative behavior, all non-trivial trajectories dissipate energy. A characterization of such behaviors is given in terms of properties of the one- and two-polynomial matrices...
A note on persistency of excitation (2005)
Willems, Jan C., Rapisarda, Paolo, Markovsky, Ivan
We prove that if a component of the response signal of a controllable linear time-invariant system is persistently exciting of sufficiently high order, then the windows of the signal span the full...
Conserved- and zero-mean quadratic quantities in oscillatory systems (2005)
Rapisarda, Paolo, Willems, Jan C.
We study quadratic functionals of the variables of a linear oscillatory system and their derivatives. We show that such functionals are partitioned in conserved quantities and in trivially- and...
Algorithms for deterministic balanced subspace identification (2005)
Markovsky, Ivan, Willems, Jan C., Rapisarda, Paolo
New algorithms for identification of a balanced state space representation are proposed. They are based on a procedure for the estimation of impulse response and sequential zero input responses...
Totally dissipative systems (2005)
Kaneko, Osamu, Takaba, Kiyotsugu, Rapisarda, Paolo
In a totally dissipative behavior, all non-trivial trajectories dissipate energy. A characterization of such behaviors is given in terms of properties of the one- and two-polynomial matrices...
A note on persistency of excitation (2005)
Willems, Jan C., Rapisarda, Paolo, Markovsky, Ivan
We prove that if a component of the response signal of a controllable linear time-invariant system is persistently exciting of sufficiently high order, then the windows of the signal span the full...
Conserved- and zero-mean quadratic quantities in oscillatory systems (2005)
Rapisarda, Paolo, Willems, Jan C.
We study quadratic functionals of the variables of a linear oscillatory system and their derivatives. We show that such functionals are partitioned in conserved quantities and in trivially- and...
Algorithms for deterministic balanced subspace identification (2005)
Markovsky, Ivan, Willems, Jan C., Rapisarda, Paolo
New algorithms for identification of a balanced state space representation are proposed. They are based on a procedure for the estimation of impulse response and sequential zero input responses...
Totally dissipative systems (2005)
Kaneko, Osamu, Takaba, Kiyotsugu, Rapisarda, Paolo
In a totally dissipative behavior, all non-trivial trajectories dissipate energy. A characterization of such behaviors is given in terms of properties of the one- and two-polynomial matrices...
A note on persistency of excitation (2005)
Willems, Jan C., Rapisarda, Paolo, Markovsky, Ivan
We prove that if a component of the response signal of a controllable linear time-invariant system is persistently exciting of sufficiently high order, then the windows of the signal span the full...
Conserved- and zero-mean quadratic quantities in oscillatory systems (2005)
Rapisarda, Paolo, Willems, Jan C.
We study quadratic functionals of the variables of a linear oscillatory system and their derivatives. We show that such functionals are partitioned in conserved quantities and in trivially- and...
Algorithms for deterministic balanced subspace identification (2005)
Markovsky, Ivan, Willems, Jan C., Rapisarda, Paolo
New algorithms for identification of a balanced state space representation are proposed. They are based on a procedure for the estimation of impulse response and sequential zero input responses...
Linear Hamiltonian behaviors and bilinear differential forms (2004)
Rapisarda, Paolo, Trentelman, Harry L.
We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems...
Linear Hamiltonian behaviors and bilinear differential forms (2004)
Rapisarda, Paolo, Trentelman, Harry L.
We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems...
Linear Hamiltonian behaviors and bilinear differential forms (2004)
Rapisarda, Paolo, Trentelman, Harry L.
We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems...
Linear Hamiltonian behaviors and bilinear differential forms (2004)
Rapisarda, Paolo, Trentelman, Harry L.
We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems...
A Note On Persistency Of Excitation (2004)
Jan C. Willems, Paolo Rapisarda, Ivan Markovsky, Bart De Moor
This report is available by anonymous ftp from ftp.esat.kuleuven.ac.be in the directory pub/sista/markovsky/reports/04-101.ps.gz K.U.Leuven, Dept. of Electrical Engineering (ESAT), Research group SCD...
Recursive exact H-infinity identification from impulse-response measurements (2003)
Kaneko, Osamu, Rapisarda, Paolo
We study the H∞-partial realization problem from a behavioral point of view; we give necessary and suffi
Recursive exact H-infinity identification from impulse-response measurements (2003)
Kaneko, Osamu, Rapisarda, Paolo
We study the H∞-partial realization problem from a behavioral point of view; we give necessary and suffi
Recursive exact H-infinity identification from impulse-response measurements (2003)
Kaneko, Osamu, Rapisarda, Paolo
We study the H∞-partial realization problem from a behavioral point of view; we give necessary and suffi
Hamiltonian and Variational Linear Distributed Systems (2002)
Rapisarda, Paolo, Trentelman, Harry L.
We use the formalism of bilinear- and quadratic differential forms in order to study Hamiltonian and variational linear distributed systems. It was shown in [1] that a system described by ordinary...
Hamiltonian and Variational Linear Distributed Systems (2002)
Rapisarda, Paolo, Trentelman, Harry L.
We use the formalism of bilinear- and quadratic differential forms in order to study Hamiltonian and variational linear distributed systems. It was shown in [1] that a system described by ordinary...
Hamiltonian and Variational Linear Distributed Systems (2002)
Rapisarda, Paolo, Trentelman, Harry L.
We use the formalism of bilinear- and quadratic differential forms in order to study Hamiltonian and variational linear distributed systems. It was shown in [1] that a system described by ordinary...
The behavioral approach to systems and modeling (2002)
Rapisarda, Paolo, Trentelman, Harry L.
An introduction to behavioral system theory, and a brief review of the content of the Special Issue are given.
The behavioral approach to systems and modeling (2002)
Rapisarda, Paolo, Trentelman, Harry L.
An introduction to behavioral system theory, and a brief review of the content of the Special Issue are given.
The behavioral approach to systems and modeling (2002)
Rapisarda, Paolo, Trentelman, Harry L.
An introduction to behavioral system theory, and a brief review of the content of the Special Issue are given.
Balanced state representations with polynomial algebra (2002)
Willems, Jan C., Rapisarda, Paolo
Algorithms are derived which pass directly from the differential equation describing the behavior of a finite-dimensional linear system to a balanced state representation
Balanced state representations with polynomial algebra (2002)
Willems, Jan C., Rapisarda, Paolo
Algorithms are derived which pass directly from the differential equation describing the behavior of a finite-dimensional linear system to a balanced state representation
Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation (2001)
Trentelman, Harry L., Rapisarda, Paolo
We study the existence of positive and negative semidefinite solutions of algebraic Riccati equations (ARE) corresponding to linear quadratic problems with an indefinite cost functional. The problem...
A two-variable approach to solve the polynomial Lyapunov equation (2001)
Peeters, Ralf, Rapisarda, Paolo
A two-variable polynomial approach to solve the one-variable polynomial Lyapunov equation is proposed. Lifting the problem from the one-variable to the two-variable context allows to use Faddeev-type...
Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation (2001)
Trentelman, Harry L., Rapisarda, Paolo
We study the existence of positive and negative semidefinite solutions of algebraic Riccati equations (ARE) corresponding to linear quadratic problems with an indefinite cost functional. The problem...
A two-variable approach to solve the polynomial Lyapunov equation (2001)
Peeters, Ralf, Rapisarda, Paolo
A two-variable polynomial approach to solve the one-variable polynomial Lyapunov equation is proposed. Lifting the problem from the one-variable to the two-variable context allows to use Faddeev-type...
Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation (2001)
Trentelman, Harry L., Rapisarda, Paolo
We study the existence of positive and negative semidefinite solutions of algebraic Riccati equations (ARE) corresponding to linear quadratic problems with an indefinite cost functional. The problem...
A two-variable approach to solve the polynomial Lyapunov equation (2001)
Peeters, Ralf, Rapisarda, Paolo
A two-variable polynomial approach to solve the one-variable polynomial Lyapunov equation is proposed. Lifting the problem from the one-variable to the two-variable context allows to use Faddeev-type...
State maps for linear systems (1997)
Rapisarda, Paolo, Willems, Jan C.
Modeling of physical systems consists of writing the equations describing a phenomenon and yields as a result a set of differential-algebraic equations. As such, state-space models are not a natural...
State maps for linear systems (1997)
Rapisarda, Paolo, Willems, Jan C.
Modeling of physical systems consists of writing the equations describing a phenomenon and yields as a result a set of differential-algebraic equations. As such, state-space models are not a natural...