Analysis and synthesis of uncertain switched discrete-time systems

The problems of L₂-gain analysis and control synthesis for a class of linear discrete-time switched systems with convex-bounded parameter uncertainties in all system matrices are investigated. The main thrust is based on the constructive use of an appropriate switched Lyapunov functional. The L₂-gain analysis is to characterize conditions under which the linear switched system with polytopic uncertainties is uniformly quadratically stable with an L₂ gain smaller than a prescribed constant level. The control synthesis is to design switched feedback schemes, whether based on state-, output measurements or by using dynamic output feedback, to guarantee that the corresponding closed-loop system enjoys the uniform quadratic stability with an L₂ gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over linear matrix inequalities and tested on representative examples.