Analysis of Uncertain Discrete-Time Linear Periodic Systems based on System Lifting and LMIs

In this article, we propose novel linear matrix inequality (LMI) conditions for the stability and l2 gain performance analysis of discrete-time linear periodically time-varying (LPTV) systems. These LMIs are convex with respect to all of the coefficient matrices of the LPTV systems and this property is promising when we deal with several control system analysis and synthesis problems. For example, we can apply those LMIs straightforwardly to robust performance analysis problems of LPTV systems that are affected by polytopic-type uncertainties. Even though our approach for robust performance analysis is conservative in general, we can reduce the conservatism gradually by artificially regarding the original N-periodic system as pN-periodic and increasing p. In addition, thanks to the simple structure of the LMI conditions, we can readily derive a viable test to verify the exactness of the computation results.