State feedback stabilization of a class of uncertain periodic systems

Abstract

AbstractThis paper deals with the robust stability and stabilization problem for a class of uncertain linear periodic discrete time system. This class is defined as the class of systems subject, at first, to LFR (Linear fractional representation)-based uncertainty and then to LFR and polytopic uncertainties together. The LFR-based uncertainty encompasses the case of norm bounded uncertainty as a special case. The use of a full block S-procedure allows to reformulate the stability LMI conditions of an uncertain system through a dual form of quadratic Lyapunov inequality in equivalent efficient LMI conditions that can be easily checked by any LMI solver.The obtained conditions are then used to propose a periodic state feedback controller ensuring the robust stabilizability of the obtained closed loop system. The use of the PDLF (parameter-dependent Lyapunov functions) technique enables one to take account in the same time of polytopic uncertainties. Numerical examples are provided to illustrate the proposed results.