This paper studies the finite-time H∞control problem of T-S fuzzy systems subject to external disturbances. A novel fuzzy control approach is developed on the basis of the control Lyapunov function technique and the finite-time Lyapunov theorem so that the closed-loop fuzzy system is finite-time stable with guaranteed H∞performance. It is shown that the proposed control approach does not require the existence of a Lyapunov function before design of the fuzzy controller in comparison with many existing control approaches to finite-time control of nonlinear systems via the technique of control Lyapunov functions, and thus, the finite-time controller and the corresponding Lyapunov function can be designed simultaneously. The procedures on how to obtain the fuzzy controller are provided in terms of linear matrix inequalities. Moreover, an upper bound on the time taken for state trajectories to arrive at their desired targets is estimated. The effectiveness of the proposed finite-time H∞control approach is finally illustrated via numerical simulations.

This paper studies the adaptive finite-time stabilization problem for a class of nonlinear systems described by Takagi-Sugeno (T-S) fuzzy dynamic models with parametric uncertainties. A novel adaptive state feedback control scheme for the T-S fuzzy systems is proposed, and the scheme is developed based on finite-time Lyapunov theorem and adaptive backstepping-like method. Augmented dynamics are introduced in the design of finite-time stabilization controllers to construct suitable finite-time Lyapunov functions. It is shown that finite-time convergence of the closed-loop adaptive control system can be achieved, and the potential controller singularity problem caused by the augmented dynamics can be avoided. In addition, constructive procedures to obtain such an adaptive finite-time controller are given. Convergence time as a transient performance specification is also taken into account, and a finite upper bound on the convergence time is estimated. Finally, two numerical examples are provided to illustrate the effectiveness and practicality of the proposed adaptive control approach.

This paper considers the finite-time stabilization problem for a class of nonlinear systems that can be described by Takagi-Sugeno (T-S) fuzzy models. We propose a novel finite-time switching fuzzy control scheme for T-S fuzzy models, and the scheme is based on the Lyapunov stability theory and the control Lyapunov function technique. It is shown that the finite-time fuzzy controller and the quadratic control Lyapunov function can be obtained at the same time by solving a set of linear matrix inequalities, which can be easily facilitated by available software packages. It is also shown that the potential control law singularity can be avoided with the proposed control scheme. Unlike many existing approaches to finite-time stabilization of general nonlinear systems, the proposed approach does not require the restrictive assumption on the existence of a control Lyapunov function before the corresponding control law is constructed. Furthermore, a finite upper bound on the settling time is estimated, which indicates that within the settling time, the system trajectory would arrive and stay at the origin thereafter. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.