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 admissible uncertainties. A linear matrix inequality (LMI)-based analysis result is derived. The synthesis problem is to design linear state-feedback and dynamic output-feedback controllers that robustly stabilize the uncertain discrete-time system and achieve the strict positive realness for the closed-loop transfer functions. It has been established that the problems above can be cast into a class of parameterized strict positive real control problems without uncertainties.
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