LMI characterizations of positive realness and static output feedback positive real control of discrete-time systems

This paper is concerned with the problems of positive real analysis and control synthesis for discrete-time systems. New linear matrix inequality (LMI) characterizations of positive realness are derived, which enable one to check the positive realness by using parameter-dependent Lyapunov function. The relationship between the proposed characterizations and the existing ones are clarified, which shows that our new results are of less conservatism for characterizing the positive realness of discrete-time systems with polytopic uncertainty. In addition, sufficient conditions for static output feedback positive real controller design are given in terms of solutions to a set of linear matrix inequalities. Numerical examples are included for illustration.