Positive realness of a class of uncertain linear discrete-time systems with constant state delay

This paper is concerned with the problems of positive real analysis and control synthesis for discrete-time systems with time-invariant state delay and parameter uncertainties. Motivated by the results of, linear matrix inequality (LMI) characterizations of positive realness for discrete delay systems with/without uncertainties are derived, which enable one to check the positive realness by using parameter-dependent Lyapunov function. Numerical examples are included for illustration.