Design of stabilizing strategies for discrete time linear systems dual switching

Discrete-time dual switching linear systems are piecewise linear systems subject to both stochastic and deterministic commutations. Stochastic jumps, well-suited to account for unpredictable events like faults or abrupt changes in the parameters, are modeled by means of a Markov chain. The deterministic switches are dictated by a scheduling signal, used as a control variable in order to achieve stochastic stability and guaranteed input/output performance. We derive sufficient conditions for the existence of a state-feedback switching law attaining these goals. Further, the more challenging co-design problem is addressed, namely the joint synthesis of a linear state-feedback controller and a stabilizing switching strategy ensuring a prescribed performance. The results are illustrated by means of a numerical example concerning a networked control system under occasional communication failures.