Positive-realness analysis of sampled-data systems and its applications

The paper is concerned with positive-realness of sampled-data systems. We first review a few slightly different notions of positive-realness of sampled-data systems, and clarify their mutual relationships. We then focus on so-called strong positive-realness among them, and introduce a measure called the positive-realness gap index. We show that this index can be computed quite efficiently with a bisection method, and provide state space formulas for its computation. The importance of this index lies in that it is quite useful for stability analysis of sampled-data systems. This is demonstrated with the nonlinear stability analysis as well as the gain margin analysis, or a sort of stability radius analysis