On the Hautus test for exponentially stable $C_0$-groups (2009)
For finite-dimensional systems the Hautus test is a well-known and easy checkable condition for observability. Russell and Weiss [SIAM J. Control Optim, 32 (1994), pp. 1--32] suggested an...
Van Mourik, S., Zwart, H.J., Keesman, K.J.
For chemical reactors with non-linear fluid dynamics, a linear model realisation is proposed. The inputs are the ingoing concentration of a certain component in the fluid, and the reaction rate. The...
System theoretic properties of a class of spatially invariant systems (2009)
Curtain, R., Iftime, O.V., Zwart, H.J.
In this paper we develop new readily testable criteria for system theoretic properties such as stability, controllability, observability, stabilizability and detectability for a class of spatially...
Exponential stability of a class of boundary control systems (2009)
Villegas, J.A., Zwart, H.J., Le Gorrec, Y., Maschke, B.
We study a class of partial differential equations (with variable coefficients) on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we provide...
Integrated open loop control and design of a food storage room (2009)
Usually, control design in a food storage room takes place after the plant has been designed. However, the performance of the plant connected to the controller might be improved by simultaneous...
The growth of a $C_0$-semigroup characterised by its cogenerator (2008)
We characterise contractivity, boundedness and polynomial growth for a $C_0$-semigroup in terms of its cogenerator $V$ (or the Cayley transform of the generator) or its resolvent. In particular, we...
System theoretic properties of platoon-type systems (2008)
Curtain, R.F., Iftime, O.V., Zwart, H.J.
This paper presents readily checkable criteria for several system theoretic properties (stability, approximate and exact controllability, exponential stabilizability) for a particular class of...
The duality of orogenic belts (2007)
world is proposed, based in first instance on the facies series of the metamorphic rocks. The Hercynian and Alpine orogens of Europe are reviewed in detail and are found to differ respectively in...
Is $A^{-1}$ an infinitesimal generator? (2007)
In this paper we study the question whether $A^{-1}$ is the infinitesimal generator of a bounded $C_0$-semigroup if $A$ generates a bounded $C_0$-semigroup. If the semigroup generated by $A$ is...
Crank-Nicolson scheme for abstract linear systems (2007)
This paper studies the Crank-Nicolson discretization scheme for abstract differential equations on a general Banach space. We show that a time varying discretization of a bounded analytic...
A note on plynomially bounded $C_0$-semigroups (2007)
We characterize polynomial growth of a $C_0$-semigroup in terms of the first power of the resolvent of its generator. We do this for a class of semigroups which includes $C_0$-semigroups on Hilbert...
Growth estimates for $\exp(A^{-1}t)$ on a Hilbert space (2007)
Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on the Hilbert space $H$. Since $A^{-1}$ is a bounded operator, it is the infinitesimal generator of a...
Modeling and control of water disinfection process in annular photoreactors (2007)
Keesman, K.J., Vries, D., Van Mourik, S., Zwart, H.J.
As an alternative or addition to complex physical modeling, in this paper transfer function models of the disinfection process in annular photoreactors under different flow conditions are derived....
The Cayley transform of the generator of a bounded $C_0$-semigroup (2007)
Let $A$ be the generator of a uniformly bounded $C_0$-semigroup on the Banach space $X$. We present sufficient conditions on the resolvent $(A-\lambda I)^{-1},$ $Re(\lambda)>0,$ under which the...
Modelling and controller design for a UV disinfection plant (2007)
Van Mourik, S., Geurts, B.J., Zwart, H.J.
A mathematical model describing fluid flow and concentration dynamics of microorganisms inside a UV photoreactor is developed. Using physical arguments and techniques from system theory, we...
Van Mourik, S., Zwart, H.J., Keesman, K.J.
For a class of scalar nonlinear systems with switching input a controller is designed using design theory for linear systems. A stability criterion is derived that contains all the physical system...
Analytic control law for a food storage room (2007)
Van Mourik, S., Zwart, H.J., Keesman, K.J.
A storage room contains a bulk of potatoes that produce heat due to respiration. A ventilator blows cooled air around to keep the potatoes cool and prevent spoilage. The aim is to design a control...
Vries, D., Keesman, K., Zwart, H.J.
A linear regressive model structure and output predictor, both in algebraic form, are deduced from an LTI state space system with certain properties without the need of direct matrix inversion. On...
Vries, D., Keesman, K.J., Zwart, H.J.
In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its...
n this paper we investigate and compare the properties of the semigroup generated by $A$, and the sequence $A_d^n$, $n \in {\mathbb N}$, where $A_d= (I+A)(I-A)^{-1}$. We show that if $A$ and $A^{-1}$...
Well-posedness and regularity for a class of hyperbolic boundary control systems (2006)
Zwart, H.J., Le Gorrec, Y., Maschke, B.M.J., Villegas, J.A.
We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show this class of...
Continuous-time Kreiss resolvent condition on infinite-dimensional spaces (2006)
Given the infinitesimal generator $A$ of a $C_0$-semigroup on the Banach space $ X$ which satisfies the Kreiss resolvent condition, i.e., there exists an $ M>0$ such that $ \Vert (sI-A)^{-1}\Vert...
Climate control of a bulk storage room for foodstuffs (2006)
Van Mourik, S., Zwart, H.J., Keesman, K.J.
A storage room contains a bulk of potatoes that produce heat due to respiration. A ventilator blows cooled air around to keep the potatoes cool and prevent spoilage. The aim is to design a control...
Villegas, J.A., Le Gorrec, Y., Zwart, H.J., Maschke, B.M.J.
In this paper we study a class of partial differential equations (PDE's), which includes Sturm-Liouville systems and diffusion equations. From this class of PDE's we define systems with control and...
On Approximate Observability of Strongly Stable Systems (2006)
The Hautus test of Russelll and Weiss is sufficient for approximately observability when the system is exponentially stable. By means of an example we show that this does not hold when the system is...
Composition of infinite-dimensional Dirac structures (2006)
Kurula, M., Van Der Schaft, A.J., Zwart, H.J.
In this paper, we define the Dirac structure and give some fundamental tools for its study.We then proceed by defining composition of ``split Dirac structures''. In the finite-dimensional case,...
Dissipative boundary control systems with application to distributed parameters reactors (2006)
Le Gorrec, Y., Maschke, B.M.J., Villegas, J.A., Zwart, H.J.
In this paper we consider distributed parameter physical systems composed of a reversible part associated with a skew-symmetric operator J as Hamiltonian systems and a symmetric operator associated...
Stability and Stabilization of a Class of Boundary Control Systems (2005)
Villegas, J.A., Zwart, H.J., Le Gorrec, Y., Maschke, B.M.
We study a class of partial differential equations on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we describe how to obtain an impedance...
Stability and Stabilization of a Class of Boundary Control Systems (2005)
Villegas, MSc. J.A., Zwart, Dr. H.J., Le Gorrec, Y., Maschke, Dr. B.M., Schaft Van Der, Prof.dr. A.J.
We study a class of partial differential equations on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we describe how to obtain an impedance...
Stability and Stabilization of a Class of Boundary Control Systems (2005)
Villegas, J.A., Zwart, H.J., Le Gorrec, Y., Maschke, B.M., Schaft Van Der, A.J.
We study a class of partial differential equations on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we describe how to obtain an impedance...
Iftime, O.V., Zwart, H.J., Curtain, R.F.
We obtain a representation of all self-adjoint solutions of the control algebraic Riccati equation associated to the infinite-dimensional state linear system Σ(A,B,C) under the following...
Boundary Control Systems and the System Node (2005)
Villegas, J.A., Le Gorrec, Y., Zwart, H.J.
In this paper we show how to formulate a boundary control system in terms of the system node, that is, as an operator $ \mathcal{S}:= \left[ \begin{smallmatrix} A\& B\, \\ C\& D...
Port Representations of the Telegrapher's Equations (2005)
Villegas, J.A., Zwart, H.J., Van Der Schaft, A.J.
This article studies the telegrapher's equations with boundary port variables. Firstly, a link is made between the telegrapher's equations and a skew-symmetric linear operator on a spatial domain....
Sufficient Conditions for Admissibility (2005)
Sufficient conditions for the finite and infinite-time admissibility of an observation operator are given. It is shown that the estimates of Weiss are close to being sufficient. If the semigroup is...
Le Gorrec, Y., Zwart, H.J., Maschke, B.M.J.
Associated with a skew-symmetric linear operator on the spatial domain $[a,b]$ we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac...
Tools for analysis of Dirac structures on Hilbert spaces (2004)
Golo, G., Iftime, O.V., Zwart, H.J., Van Der Schaft, A.J.
In this paper tools for the analysis of Dirac structures on Hilbert spaces are developed. Some properties are pointed out and two natural representations of Dirac structures on Hilbert spaces are...
Le Gorrec, Y., Zwart, H.J., Maschke, B.M.J.
Associated with a skew-symmetric linear operator on the spatial domain $[a,b]$ we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac...
Nehari problems and equalizing vectors for infinite-dimensional systems (2001)
For a class of infinite-dimensional systems we obtain a simple frequency domain solution for the suboptimal Nehari extension problem. The approach is via $J$-spectral factorization, and it uses the...
Guo, B.Z., Zwart, H.J., Curtain, R.F.
In this paper we investigate the relation between discrete and continuous operators. More precisely, we investigate the properties of the semigroup generated by $A$, and the sequence $A_d^n$, $n \in...
In this paper we study systems in which the system operator, $A$, has a Riesz basis of (generalized) eigenvectors. We show that this class is subset of the class of spectral operators as studied by...
On H-infinity control for dead-time systems (2000)
A mixed sensitivity H-infinity problem is solved for dead-time systems. It is shown that for a given bound on the H-infinity-norm causal stabilizing controllers exist that achieve this bound if and...
On H-infinity control for dead-time systems (2000)
Meinsma, Dr.ir. G., Zwart, Dr. H.J.
A mixed sensitivity H-infinity problem is solved for dead-time systems. It is shown that for a given bound on the H-infinity-norm causal stabilizing controllers exist that achieve this bound if and...
On H-infinity control for dead-time systems (2000)
A mixed sensitivity H-infinity problem is solved for dead-time systems. It is shown that for a given bound on the H-infinity-norm causal stabilizing controllers exist that achieve this bound if and...
The standard $H_\infty$-suboptimal control problem for LTI infinite dimensional systems (2000)
In this paper we provide sufficient conditions for the solvability of the standard $H_{\infty}$-suboptimal control problem for linear, time invariant, infinite-dimensional systems with...
Disproof of an admissibility conjecture of Weiss (2000)
Two conjectures on admissible control operators by George Weiss are disproved in this paper. One conjecture says that an operator $B$ defined on an infinite-dimensional Hilbert space $U$ is an...
J-spectral factorization and equalizing vectors (2000)
For the Wiener class of matrix-valued functions we provide necessary and sufficient conditions for the existence of a $J$-spectral factorization. One of these conditions is in terms of equalizing...
Disproof of two conjectures of George Weiss (2000)
Two conjectures that were posed by Weiss almost ten years ago are shown not to hold. The first conjecture states that a scalar operator is admissible if and only a certain resolvent estimate holds....
Sufficient conditions for admissibility (2000)
Sufficient conditions for the finite and infinite-time admissibility of an observation operator are given. It is shown that the estimates of Weiss are close to being sufficient. If the semigroup is...
Where are the zeros located? (1998)
Zwart, H.J., Blondel, V.D., Sontag, E.D., Vidyasagar, M., Willems, J.C.
Corrections and extensions of "Optimal Control of Linear Systems with Almost Periodic Inputs" (1996)
The first part of the paper concerns the existence of strongly stabilizing solutions to the standard algebraic Riccati equation for a class of infinite-dimensional systems of the form...
Curtain, R.F., Zwart, Dr. H.J.
The first part of the paper concerns the existence of strongly stabilizing solutions to the standard algebraic Riccati equation for a class of infinite-dimensional systems of the form...
The first part of the paper concerns the existence of strongly stabilizing solutions to the standard algebraic Riccati equation for a class of infinite-dimensional systems of the form...
Kuiper Zwart, C. R. Kuiper, H. J. Zwart
The algebraic Riccati equation (ARE) has been studied in great detail for finite-dimensional systems. For infinite-dimensional systems almost all results concentrate on the relation with the linear...
Stability is realization-dependent: some examples (1995)
Zwart, H.J., Yamamoto, Y., Gotoh, Y.
This paper gives some examples with the same impulse response, both approximately controllable and observable, but one of them is exponentially stable and the other is unstable. Some related spectral...
Stability is realization-dependent: some examples (1995)
Zwart, Dr. H.J., Yamamoto, Y., Gotoh, Y.
This paper gives some examples with the same impulse response, both approximately controllable and observable, but one of them is exponentially stable and the other is unstable. Some related spectral...
An introduction to infinite-dimensional linear systems theory / Ruth F. Curtain, Hans Zwart (1995)
Curtain, Ruth F., Zwart, H. J. (Hans J.)
Incluye bibliografía e índice
Stability is realization-dependent: some examples (1995)
Zwart, H.J., Yamamoto, Y., Gotoh, Y.
This paper gives some examples with the same impulse response, both approximately controllable and observable, but one of them is exponentially stable and the other is unstable. Some related spectral...
Stability of perturbed linear distributed parameter systems (1991)
We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an...
Stability of perturbed linear distributed parameter systems (1991)
We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an...
Stability of perturbed linear distributed parameter systems (1991)
We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an...
Geometric theory for infinite dimensional systems / H. J. Zwart (1989)
Incluye bibliografía e índice