State-feedback stabilization for nonlinear time-delay systems:a new fuzzy weighting-dependent Lyapunov-Krasovskii functional approach

Abstract

This paper concentrates upon a new stabilization for nonlinear time-delay systems via the Takagi-Sugeno (TS) fuzzy model approach. At first, we represent a nonlinear time-delay system as a kind of neutral-type TS fuzzy systems with a block delay. And then, we propose a new fuzzy weighting-dependent Lyapunov-Krasovskii functional (FWD-LKF), which directly includes the fuzzy weighting functions. Based on the new FWD-LKF, a new fuzzy state-feedback controller consisting not only of the state but also of the delay-feedback block is proposed about linear matrix inequalities (LMIs). Especially the size of the time-delay is available, the delayed-feedback block plays a very significant role in improving the stabilization of the system. Furthermore using an improved relaxation technique, this paper suggests another new state-feedback controller which improves the flexibility of the proposed controller. As a result, the suggested criterion is more effective than the existing criterion derived by conventional approaches. These concepts would be applicable to designing the guaranteed cost controller, the min-max controller, the robust controller against system uncertainties, and so on.