Stabilization of linear switched delay systems: ℋ2 and ℋ∞ methods

Abstract

This paper presents new results pertaining to the delay-dependent stability and control synthesis of a class of linear switched continuous-time systems with time-varying delays. A new state transformation is introduced to exhibit the delay-dependent dynamics in the slow-time scale. For stability, we construct an appropriate selective Lyapunov functional to derive delay-dependent LMI-based sufficient conditions under arbitrary switching and without relying to overbounding. For the control synthesis, we design switched feedback schemes based on quadratic ℋ2, ℋ∞ and simultaneous ℋ2/ℋ∞ performance criteria. Under the developed transformation, it is established that both the instantaneous and delayed feedback control yield identical results. Numerical examples are presented to illustrate the analytical development.