Robust output stabilization: improving performance via supervisory control

TL;DR

This paper develops supervisory control strategies to maintain input-output stability in switched systems, enhancing performance in observer design and chaotic oscillator synchronization.

Contribution

It introduces dwell-time and hysteresis supervisors for stability, applying them to observer design and chaotic oscillator synchronization.

Findings

Supervisory strategies ensure stability under switching.

Hybrid observer achieves fast convergence with low overshoot.

Control effort is reduced in synchronized chaotic oscillators.

Abstract

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.