Passivity-based switching rule and control law co-design of networked switched systems with feedback delays

Abstract

In this chapter, a class of switched linear systems under a hybrid state feedback controller with time-varying delays is studied. The main contribution is given on the issue of how to co-design switching rule and feedback control law so as to make the closed-loop system strictly input feed-forward output-feedback passive for all admissible time delays in the feedback channels. We derive the sufficient conditions for strict input feed-forward, output-feedback passification of switched systems with time-varying delays under some state-dependent switching rule by using the method of multiple storage functions. The proposed switching rule can achieve strict input feed-forward, output-feedback passivity of the switched delay systems, whose subsystems are all allowed to be input feed-forward output-feedback nonpassive. The finite–gain L 2 stability in closed-loop is achieved in this way. Furthermore, under the proposed switching rule the asymptotic stability can be guaranteed if the switched system is zero-state detectable when exogenous disturbance input is zero. Finally, we present an algorithm on how to co-design switching rule and feedback control law to maintain strict input feed-forward output-feedback passivity of switched systems with time-varying delays.