Given a stable square plant G 1(s), based on linear matrix inequality (LMI) method, necessary and sufficient conditions are presented for the existence of a stable multiplier G 2(s) such that G 1(s)G 2(s) is extended strictly positive real (ESPR). Furthemore, for uncertain plants, the corresponding problems are considered and solved. An application to the study of dichotomy for pendulum-like systems is also presented. Examples are given to illustrate the results.
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Duan et al. (2004) studied this question.
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