Periodically Time-Varying Memory State-Feedback Controller Synthesis for Uncertain Discrete-Time Linear Systems

The H2 Case

Abstract

This study is concerned with the synthesis of periodically time-varying memory state-feedback controllers (PTVMSFCs) for discrete-time linear systems. In our preceding studies, we have already established basic strategies for LMI-based (robust) H-infinity PTVMSFCs synthesis, and in this paper we extend those results to the H2 performance criterion. In the H2 case, the main difficulty stems from the fact that we have to ensure the existence of a common solution for multiple LMI conditions that are related to Lyapunov inequality and inequalities for bounding traces of Lyapunov matrix. We overcome this difficulty by deriving an analytic representation of LMI solutions and derive a necessary and sufficient LMI condition for the H2-PTVMSFCs synthesis. Based on these results, we also consider robust H2-PTVMSFC synthesis for polytopic-type uncertain LTI systems.