Static Output-Feedback Simultaneous Stabilization of Interval Time-Delay Systems

This paper addresses the problem of simultaneous static output-feedback stabilization of a collection of interval time-delay systems. It is shown that this problem can be converted into a matrix measure assignment problem. Sufficient conditions for guaranteeing the robust stability for considered systems are derived in term of the matrix measures of the system matrices. By using matrix inequalities, we provide two cases of obtaining a static output-feedback controller that can stabilize the system, i.e., both P I = and P I ≠ cases are considered where I is a identity matrix and P is a common positive definite matrix to guarantee the stability of the overall system. The sufficient condition with P I = is formulated in the format of linear matrix inequalities (LMIs). When P I ≠ is considered, the sufficient condition becomes a nonlinear matrix inequality problem and a heuristic iterative algorithm based on the LMI technique is presented to solve the coupled matrix inequalities. Finally, an example is provided to illustrate the effectiveness of our approach. Key-Words: Matrix measure; Robust control; Output feedback; Interval systems; Linear Matrix Inequality