On exact exponential stability assignment of retarded delay systems via static output-feedback controllers

This paper addresses the static output-feedback (SOF) exponential stabilization problem of retarded delay systems with a specification on the decay rate and decay coefficient. A novel Lyapunov-Krasovskii functional equipped with appropriate exponential terms is provided to establish a new condition for exponential stability. Based on this and an augmentation technique, a necessary and sufficient condition for quadratic SOF exact exponential stabilizability is proposed. An efficient iteration algorithm is then given to solve the proposed condition. Using the proposed approach, no structural constraints are imposed on the slack matrices when the controller matrix is parameterized, and the obtained controller not only stabilizes the original system but also guarantees that the closed-loop system possess desirable transient properties. Numerical examples are used to show the effectiveness of the theoretical result