On the analysis and synthesis of robust strict positive real systems

As the first main result, this paper presents a criterion which is very easy to be tested for robust strict positive realness of perturbed systems. Then, it considers such two problems as follows: 1) When does there exist a real polynomial, or more generally, a real transfer function B(s), such that B(s)/D(s) is strict positive real (SPR) for all D(s)∈D, D is a convex polytopic polynomial family? 2) When does there exist a compensator C(s) such that N(s)C(s)/D(s) is SPR for all N(s)∈N, D(s)∈D, N and D are both convex polytopic polynomial families? Necessary and sufficient conditions for such B(s) and C(s) to exist are given by this paper. Further the methods for synthesizing such B(s) and C(s) are also given. The results of this paper only involve computation of the extremes of N and D, and adopt diagrammatic methods like Bode plot; therefore, they are very simple and convenient to apply