Positive real analysis and synthesis of uncertain discrete time systems

The positive real analysis and synthesis problems for a class of uncertain discrete-time systems are considered. The uncertainties are expressed in a linear fractional form. The analysis problem is to characterize conditions for which the uncertain discrete-time system is positive real for all admis sible uncertainties. A linear matrix inequality (LMI)-based analysis result is derived. The synthesis problem is to design linear state-feedback and d ynamic output-feedback controllers that robustly stabilize the uncertain di screte-time system and achieve the strict positive realness for the closed- loop transfer functions. It has been established that the problems above ca n be cast into a class of parameterized strict positive real control proble ms without uncertainties.