Robust H∞ control for uncertain linear neutral delay systems

Abstract

This paper deals with the problem of robust H∞ control for uncertain linear neutral delay systems. The parameter uncertainty under consideration is assumed to be norm-bounded time-invariant and appears in all the matrices of the state-space model. The problem we address is the design of memoryless state feedback controllers such that the closed-loop system is asymptotically stable and the H∞ norm of the closed-loop transfer function from disturbance to the controlled output is strictly less than a prescribed positive scalar for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the above problem is proposed. When this matrix inequality is feasible, an explicit expression for the desired state feedback controller is given. Furthermore, a numerical example is provided to demonstrate the effectiveness of the proposed approach.