Switched Discrete-Time Delay Systems: Delay-Dependent Analysis and Synthesis

A delay-dependent analysis and synthesis approach is established for a class of linear discrete-time switched delay systems with convex bounded parameter uncertainties in all system matrices. New results are established for both constant and time-varying delays using switched Lyapunov-Krasovskii functionals. A delay-dependent analysis of the uncertain switched delay system is developed to guarantee that it is asymptotically stable with an a"'(2) gain smaller than a prescribed constant level. Delay-dependent switched control feedback is then designed, based on state and output measurements, to render the corresponding switched closed-loop system delay-dependent asymptotically stable with a prescribed a"'(2) gain measure. The developed results are cast as linear matrix inequalities (LMIs) and tested on representative examples.