Simultaneous static output-feedback stabilization for a collection of interval time-delay systems via LMI approach

This paper addresses two control design problems. First, we treat the problem of simultaneously stabilizing static output-feedback controller design for a collection of continuous-time interval time-delay systems. It is shown that this problem is solvable if a matrix measure assignment problem is solvable. We also proved that the admissible solution set of the matrix measure assignment problem is convex. Second, we focus on the simultaneous static output-feedback stabilization problem for a collection of discrete-time interval systems. It is shown that this problem is solvable if a matrix's spectral norm assignment problem is solvable. We also proved hat the admissible solution set of the matrix's spectral norm assignment problem is convex. And further, the matrix's spectral norm assignment problem or the matrix measure assignment problem is shown to be equivalent to a linear matrix inequality (LMI) feasibility problem. Finally, an example is provided to illustrate the proposed methodology.