LMI conditions for output feedback control of switched systems based on a time-varying convex Lyapunov function

This paper proposes novel sufficient conditions expressed in terms of linear matrix inequalities for the dynamical output feedback control design of discrete-time switched linear systems. More specifically, an output-dependent switching function together with a full order switched controller are determined in order to assure exponential stability and a guaranteed H2 performance level. The proposed output feedback conditions have some useful properties: (a) they are based on a time-varying convex Lyapunov function, which contributes to reducing conservatism, (b) the controller parameters are independent of the Lyapunov matrices, which lead to time-invariant controller matrices, and (c) the conditions are expressed in terms of linear matrix inequalities being easier to solve, but not necessarily more conservative than other techniques available in the literature. Two academic examples are used for validation and comparison with other techniques from the literature.