Delay-dependent robust H∞ control for uncertain singular systems with discrete and distributed delays

The problem of delay-dependent robust H_∞ control for uncertain singular systems with discrete and distributed delays is revisited in this paper. The parameter uncertainties are assumed to be norm-bounded and the time delays to be time-varying, size-bounded and derivative-bounded. Using Lyapunov-Krasovskii functional and free weighting matrix methods, a new delay-dependent bounded real lemma is presented which ensures the considered system to be regular, impulse free and globally asymptotically stable with an given H_∞ performance. On this basis, the robust H_∞ performance analysis and robust H_∞ control problem are solved and an explicit expression of the desired state-feedback controller is also given. Through matrix parametrization method, the obtained results are formulated in terms of linear matrix inequalities (LMIs) without involving decomposition of the system matrices, which makes the design procedure relatively simple and reliable. Some numerical examples are given to illustrate the effectiveness of the proposed method.