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- D. Liberzon
- 2007 Mediterranean Conference on Controlâ€¦
- 2007

This paper addresses the problem of stabilizing a nonlinear system by means of quantized output feedback. A framework is presented in which the control input is generated by an observer-based feedback controller acting on quantized output measurements. A stabilization result is established under the assumption that this observer-based controller possessesâ€¦ (More)

- J. P. Hespanha, D. Liberzon, A. R. Teel
- Proceedings of the 44th IEEE Conference onâ€¦
- 2005

This paper introduces appropriate concepts of input-to-state stability (ISS) and integral-ISS for systems with impulsive effects. We provide a set of Lyapunov-based sufficient conditions to establish these properties. When the continuous dynamics are stabilizing but the impulsive effects are destabilizing, the impulses should not occur too frequently, whichâ€¦ (More)

- Dipak Chatterjee, D. Liberzon
- 2004 43rd IEEE Conference on Decision and Controlâ€¦
- 2004

In this paper we propose a method for stability analysis of switched systems perturbed by a Wiener process. It utilizes multiple Lyapunov-like functions and is analogous to an existing result for deterministic switched systems.

- Dragan Nesic, D. Liberzon
- Proceedings of the 44th IEEE Conference onâ€¦
- 2005

We propose to use ISS small-gain theorems to analyze stability of hybrid systems. We demonstrate that the small-gain analysis framework is very naturally and generally applicable in the context of hybrid systems, and thus has a potential to be useful in many applications. The main idea is illustrated on specific problems in the context of control withâ€¦ (More)

- D. Liberzon, Dragan Nesic
- Proceedings of the 44th IEEE Conference onâ€¦
- 2005

We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with linear dynamics and quantized state measurements. Quantizers considered in this paper take finitely many values and have an adjustable "zoom" parameter. Building on an approach applied previously to systems with no disturbances,â€¦ (More)

- L. Vu, Dipak Chatterjee, D. Liberzon
- Proceedings of the 44th IEEE Conference onâ€¦
- 2005

In this paper we prove that a switched nonlinear system has several useful ISS-type properties under average dwell-time switching signals if each constituent dynamical system is ISS. This extends available results for switched linear systems. We apply our result to stabilization of uncertain nonlinear systems via switching supervisory control, and show thatâ€¦ (More)

- Saunak Mitra, D. Liberzon
- 2004 43rd IEEE Conference on Decision and Controlâ€¦
- 2004

A formal method based technique is presented for proving the average dwell time property of a hybrid system, which is useful for establishing stability under slow switching. The hybrid input/output automaton (HIOA) of Lynch et al. (2003) is used as the model for hybrid systems, and it is shown that some known stability theorems from system theory can beâ€¦ (More)

- Dipak Chatterjee, D. Liberzon
- Proceedings of the 45th IEEE Conference onâ€¦
- 2006

This article is concerned with stability analysis and stabilization of randomly switched systems with control inputs. The switching signal is modeled as a jump stochastic process independent of the system state; it selects, at each instant of time, the active subsystem from a family of deterministic systems. Three different types of switching signals areâ€¦ (More)

- L. Vu, D. Liberzon
- Proceedings of the 45th IEEE Conference onâ€¦
- 2006

We address a new problem - the invertibility problem for continuous-time switched linear systems, which is the problem of recovering the switching signal and the input uniquely given an output and an initial state. In the context of hybrid systems, this corresponds to recovering the discrete state and the input from partial measurements of the continuousâ€¦ (More)

- L. Vu, D. Liberzon
- 2007 46th IEEE Conference on Decision and Control
- 2007

We discuss stability of a loop consisting of two asynchronous switched systems, in which the first switched system influences the input and the switching signal of the second switched system and the second switched system affects the first switched system's jump map. We show that when the first switched system has a small dwell-time and is switching slowlyâ€¦ (More)