New characterization of positive realness and control of a class of uncertain polytopic discrete-time systems

This paper deals with the problems of positive real analysis and control synthesis for a class of discrete-time polytopic systems with uncertainties. The systems under consideration are modelled in a polytopic form with linear fractional uncertainties in its vertices. A new linear matrix inequality (LMI) characterization of positive realness for this class of systems is given. It enables one to check the positive realness by using parameter-dependent Lyapunov function. This new characterization exhibits a kind of decoupling between the Lyapunov matrix and the system matrices, which is subsequently exploited for control design. Based on the new result, sufficient conditions with reduced conservatism are obtained. A numerical example is also included to demonstrate the applicability of the proposed results.