Robust H_∞ control for systems with delayed state and input

The problem of robust H_∞ state feedback controller design for the generalized continuous time systems with time-varying delays in states and control inputs and parameter uncertainties residing in a polytope were investigated. A new improved performance criterion for the existence of robust H_∞ controller was presented by introducing two slack matrices. Then a H_∞ state feedback controller was derived directly from the criterion, which guarantees not only the quadratic stability of the closed-loop systems but also the H_∞ norm bound within a predefined level. The newly proposed criterion exhibits a kind of separation between the systems matrices and the positive definite Lyapunov matrices. As a result, the vertex-dependent Lyapunov functions can be adopted to deliver a less conservative result. An iterative algorithm was developed to further refine the sub-optimal controller. Moreover, this contribution addressed an effective method to obtain new criteria with less conservativeness based on existing research results. A numerical example was employed to illustrate the effect of the proposed approach.