Robust positive realness analysis and control for a class of systems with uncertainties

Robust positive realness analysis and control problem is discussed for a class of systems with a polynomial form parameter uncertainties. Analysis condition based on linear matrix inequality (LMI) under which the uncertain system is extended strictly positive real for all admissible uncertainties is characterized. A dynamic output-feedback controller is designed such that the resulting closed loop system is admissible and extended strictly positive real for all admissible uncertainties. It has been established that the above problems can be converted into a class of extended strictly positive real control problems without uncertainties.