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

In this paper, we first study strong positive-realness of sampled-data systems and introduce a measure called positive-realness gap index. We show that this index can be computed efficiently with a bisection method, and provide state space formulas for its computation. The importance of this index lies in that it is useful for robust stability analysis of sampled-data systems. An iterative procedure for computing an exact robust stability margin is given and illustrated through a numerical example.