The Passivity Control for a Kind of Uncertain T-s Fuzzy Descriptor Systems with Time-delay

We consider the problem of passivity control for a kind of T-S fuzzy system in the literature [1].We will extend it to the uncertain T-S fuzzy descriptor systems with time-delay in this paper. Generally speaking, a mathematical model cannot be used to exactly describe a dynamical system in practice because it is inevitable to include some degrees of uncertainties in the systems. Moreover, time-delay frequently occurs in various engineering systems. Time-delay and uncertainty could be the cause of instability and poor performance. In this case, we should take uncertainty and time-delay factors of the systems into account in the control design. Since the notion of passivity of energy across resistors in an electrical circuit was put forward, dissipation and passivity recognized as an important tool of studying nonlinear systems has been applied in stability analysis (see for example [2-10] and the references therein). In recent years, since descriptor systems and descriptor space perturbation theory are widely applied, the study for the descriptor systems has received much attention[11,12]. In 2000, Taniguchi, Tanaka and Wang first defined fuzzy descriptor system[13]. Fuzzy technique has been extensively used in nonlinear system control[13-15]. However, little attention has been paid to the passivity control for the uncertain T-S fuzzy descriptor with time-delay. In this paper, we considered the problem of passivity control for a kind of uncertain T-S fuzzy descriptor system with time-delay. The sufficient conditions, which