H∞ co-design for discrete-time dual switching linear systems

This paper deals with dual switching linear systems in discrete-time. Such systems have piecewise linear dynamics, with switches dictated by two different sources. One is a stochastic switching signal modeled by a Markov chain. The other is a control discrete variable to be used for stabilization and disturbance attenuation. A first main result concerns the design of switching laws guaranteeing stability and H_∞ performance. We then proceed to tackle the more challenging co-design problem, namely the joint synthesis of a linear state-feedback controller and a stabilizing switching strategy.