Robust output stabilization: improving performance via supervisory control

We analyze robust stability, in an input-output sense, of switched stable systems. The primary goal (and contribution) of this paper is to design switching strategies to guarantee that input-output stable systems remain so under switching. We propose two types of {\em supervisors}: dwell-time and hysteresis based. While our results are stated as tools of analysis they serve a clear purpose in design: to improve performance. In that respect, we illustrate the utility of our findings by concisely addressing a problem of observer design for Lur'e-type systems; in particular, we design a hybrid observer that ensures ``fast'' convergence with ``low'' overshoots. As a second application of our main results we use hybrid control in the context of synchronization of chaotic oscillators with the goal of reducing control effort; an originality of the hybrid control in this context with respect to other contributions in the area is that it exploits the structure and chaotic behavior (boundedness of solutions) of Lorenz oscillators.Comment: Short version submitted to IEEE TA

Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation.

The topic of this paper is the analysis of stability for a class of switched linear systems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions

Stability Analysis of Continuous-Time Switched Systems with a Random Switching Signal

This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part and a random part. The stochastic stability of such switched systems is studied using a Lyapunov approach. A necessary and sufficient condition is established in terms of linear matrix inequalities. The effect of the random switching signal on system stability is illustrated by a numerical example and the results coincide with our intuition.Comment: 6 pages, 6 figures, accepted by IEEE-TA