Robust H_∞ controller design for a class of linear systems with time-varying delayed state: An improved LMI approach

The problem of robust H_∞ controller design for linear systems with parameter uncertainty residing in a polytopic and time-varying delays in states is considered. A new improved LMI representation of H_∞ performance is presented for the linear systems with time-varying state delay. The state feedback H_∞ controller guarantees not only the quadratic stability of the closed-loop system but also the H_∞ norm bound within a y. The newly proposed criterion exhibits a kind of separation between the system matrices and the positive definite Lyapunov matrices. So the vertex-dependent Lyapunov functions can be adopted, and thus a less conservative result is expected to be obtained. To further refine the suboptimal controller, an iterative algorithm is developed. A numerical example is employed to illustrate the effect of the proposed approach.