Francesca Albertini, E. D. Sontag
This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control-Lyapunov function...
Meagre functions and asymptotic behaviour of dynamical systems, Nonlinear Analysis: Theory (2007)
W. Desch, H. Logemann, E. P. Ryan, Bath Ba Ay, E. D. Sontag
Abstract. A measurable function x: J ae R! X (X a metric space) is said to be C-meagre if C ae X is non-empty and, for every closed set K ae X with K " C =;, x \Gamma1 (K) has finite...
Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear systems (2007)
D. Nesic, A. R. Teel, E. D. Sontag
We provide an explicit KL stability or input-to-state stability (ISS) estimate for a sampled-data nonlinear system in terms of the KL estimate for the corresponding discrete-time system and a K...
Key words. ' Nonlinear dynamical systems, system analysis, reachability, observability, canonical systems. applied algebra.
Uniform global asymptotic stability of differential inclusions (2007)
D. Angeli, B. Ingalls, E. D. Sontag, Y. Wang
Stability of differential inclusions defined by locally Lipschitz compact valued maps is addressed. It is shown that if such a differential inclusion is globally asymptotically stable, then in fact...
Singular Trajectories in Multi-Input Time-Optimal (2007)
Problems Application To, M. Chyba, N. E. Leonard, E. D. Sontag
This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with...
Jovanovic, M. R., Arcak, M., Sontag, E. D.
A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which...
Input-to-state stabilization of linear systems with quantized state measurements (2007)
Abstract This paper considers the problem of stabilization of linear systems for which only the magnitudes of outputs are measured. It is shown that, if a system is controllable and observable, then...
Input-to-State Stabilization of Linear Systems with Positive Outputs (2007)
This paper considers the problem of stabilization of linear systems for which only the magnitudes of outputs are measured. It is shown that, if a system is controllable and observable, then one can...
Computational aspects of feedback in neural circuits (2006)
Maass, Wolfgang, Joshi, Prashant, Sontag, E. D.
It had previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with...
Abstract. This paper further develops a method, originally introduced by Angeli and the second author, for proving global attractivity of steady states in certain classes of dynamical systems. In...
Nonlinear norm-observability notions and stability of switched systems (2005)
Hespanha, Joao P, Liberzon, D, Angeli, D, Sontag, E D
This paper proposes several definitions of "norm-observability" for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the...
On the stability of Murray's testosterone model (2004)
We prove the global asymptotic stability of a well-known delayed negative-feedback model of testosterone dynamics, which has been proposed as a model of oscillatory behavior. We establish stability...
Separation principles for input-output and integral-input to state stability (2004)
D. Angeli, B. Ingalls, E. D. Sontag, Y. Wang
Abstract. We present new characterizations of input-output-to-state stability. This is a notion of detectability formulated in the ISS framework. Equivalent properties are presented in terms of...
Separation principles for input-output and integral-input to state stability (2004)
D. Angeli, B. Ingalls, E. D. Sontag, Y. Wang
We present new characterizations of input-output-to-state stability. This is a notion of detectability formulated in the ISS framework. Equivalent properties are presented in terms of asymptotic...
Separation Principles for Input-Output and Integral-Input-to-State Stability (2004)
D. Angeli, B. Ingalls, E. D. Sontag, Y. Wang
We present new characterizations of input-output-to-state stability. This is a notion of detectability formulated in the ISS (input-to-state stability) framework. Equivalent properties are presented...
Uniform Global Asymptotic Stability of Differential Inclusions (2004)
D. Angeli, B. Ingalls, E. D. Sontag, Y. Wang
Stability of di#erential inclusions defined by locally Lipschitz compact valued mappings is considered. It is shown that if such a di#erential inclusion is globally asymptotically stable, then, in...
Chyba, M., Leonard, N. E., Sontag, E. D.
This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with...
For Differential Equations with r Parameters, 2r+1 Experiments Are Enough for Identification (2002)
Given a set of differential equations... This paper shows that the best possible answer (assuming exact measurements) is 2r+1 experiments, where r is the number of parameters. Moreover, a generic set...
Meagre Functions and Asymptotic Behaviour of Dynamical Systems (2001)
W. Desch, H. Logemann, E. P. Ryan, E.D. Sontag
A measurable function x : J ae R! X (X a metric space) is said to be C-meagre if C ae X is non-empty and, for every closed set K ae X with K " C = ;, x \Gamma1 (K) has finite Lebesgue measure....
Further equivalences and semiglobal versions of integral input to state stability, Dynam (2000)
David Angeli, E. D. Sontag, Y. Wang
This paper continues the study of the integral input-to-state stability (iiss) property. It is shown that the iiss property is equivalent to one which arises from the consideration of mixed norms on...
Further equivalences and semiglobal versions of integral input to state stability, Dynam (2000)
David Angeli, E. D. Sontag, Y. Wang
This paper continues the study of the integral input-to-state stability (iiss) property. It is shown that the iiss property is equivalent to one which arises from the consideration of mixed norms on...
Further Results on Controllability of Recurrent Neural Networks (1999)
This paper studies controllability properties of recurrent neural networks. The new contributions are: (1) an extension of a previous result to a slightly different model, (2) a formulation and proof...
Clocks and Insensitivity to Small Measurement Errors (1999)
This paper provides a precise result which shows that insensitivity to small measurement errors in closed-loop stabilization can be attained provided that the feedback controller ignores observations...
Asymptotic Controllability Implies Feedback Stabilization (1999)
F.H. Clarke, Yu. S. Ledyaev, E.D. Sontag, A. I. Subbotin
It is shown that every asymptotically controllable system can be globally stabilized by means of some (discontinuous) feedback law. The stabilizing strategy is based on pointwise optimization of a...
Closed-loop identification and self-tuning (1998)
Polderman, J.W., Blondel, V.D., Sontag, E.D., Vidyasagar, M., Willems, J.C.
Where are the zeros located? (1998)
Zwart, H.J., Blondel, V.D., Sontag, E.D., Vidyasagar, M., Willems, J.C.
On chaotic observer design (1998)
Nijmeijer, H., Blondel, V.D., Sontag, E.D., Vidyasagar, M., Willems, J.C.
A Characterization of Integral Input to State Stability (1998)
David Angeli, E.D. Sontag, Yuan Wang
The notion of input to state stability (iss) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum...
A Characterization of Integral Input to State Stability (1998)
David Angeli, E. D. Sontag, Yuan Wang
Just as input to state stability (iss) generalizes the idea of finite gains with respect to supremum norms, the new notion of integral input to state stability (iiss) generalizes the concept of...
Continuous Control-Lyapunov Functions for Asymptotically Controllable Time-Varying Systems (1997)
Francesca Albertini, E.D. Sontag
This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control-Lyapunov function...
Remarks on Stabilization and Input-to-State Stability (1989)
This paper describes how notions of input-to-state stabilization are useful when stabilizing cascades of systems. 1 Introduction Consider a cascade as follows: (CAS) ( x = f(x; y) y = g(y; u) where f...
Further Equivalences and Semiglobal Versions of Integral Input to State Stability
David Angeli, E. D. Sontag, Y. Wang
This paper continues the study of the integral input-to-state stability (iiss) property. It is shown that the iiss property is equivalent to one which arises from the consideration of mixed norms on...
A Small-Gain Theorem for Almost Global Convergence of Monotone Systems
D. Angeli, P. De Leenheer, E.D. Sontag
A small-gain theorem is presented for almost global stability of monotone control systems which are open-loop almost globally stable, when constant inputs are applied. The theorem assumes...