Delay-dependent robust H∞ control of time-delay systems

In this study, a delay-dependent H_∞ performance criterion that possess decoupling structure is derived for a class of time-delay systems. It is then extended to H_∞ state-feedback synthesis for time-delay systems with polytopic uncertainty and multichannel H_∞ dynamic output-feedback synthesis for time-delay systems. All the conditions are given in terms of the linear matrix inequalities. In some previous descriptor methods, the products of controller matrices and Lyapunov matrices are completely separated in performance analysis, whereas it is not the case in controller synthesis. However, with the method in the paper, the weakness is eliminated. Numerical examples illustrate the effectiveness of our solutions as compared to results obtained by other methods.