Stability and stabilization of switched linear discrete-time systems with polytopic uncertainties

In this paper, the problems of stability and stabilization of switched linear discrete-time systems with polytopic uncertainties are investigated. A switched parameter-dependent quadratic Lyapunov function is proposed, by which the stability conditions are derived and formulated in terms of a set of linear matrix inequalities. Based on the stability result, control synthesis is then considered and a stabilizing state-feedback controller is obtained by solving a convex optimization problem subject to linear matrix inequalities. Both mode-dependent and parameter-dependent ideas are used in stability analysis and controller design for the underlying systems. Numerical examples are given to show the less conservativeness and the potential of the obtained theoretic results