Design of stabilizing strategies for dual switching stochastic-deterministic linear systems

Dual switching linear systems are systems with piecewise linear dynamics governed by two distinct external switching signals. In this paper one switching signal is stochastic and modeled as a time-homogeneous Markov chain, and the second one is assumed to be a control signal taking values in a finite set. This situation arises, for instance, in multi-loop networked control systems (NCS) with limited transmission capacity and lossy communication channels, where the control variable is the scheduling signal and the stochastic switching accounts for packet dropout. The aim of this paper is to derive suitable switching strategies for dual switching linear systems, ensuring mean-square stability and attaining guaranteed bounds on ℋ2 and ℋ∞ performance indices. The relevant sufficient conditions are expressed in terms of feasibility of sets of coupled matrix inequalities. The application to a scheduling design problem in NCS's is also discussed.