An Approach to Finite-Time $\mathcal{H}_{\infty}$ Control of T-S Fuzzy Systems via Piecewise Lyapunov Functions

This paper addresses the problem of finite-time
$\mathcal{H}_{\infty}$
control of Takagi-Sugeno (T-S) fuzzy models. By using the piecewise Lyapunov function and the finite-time Lyapunov theorem, a new controller design scheme is proposed such that the closed-loop fuzzy control system is finite-time stable with
$\mathcal{H}_{\infty}$
performance. It is shown that the proposed controller and its corresponding piecewise Lyapunov function, which is continuous across subspace boundaries, can be designed by solving a set of bilinear matrix inequalities (BMIs). Moreover, an upper bound on the time required for finite-time convergence of the fuzzy control system can be estimated. Finally, numerical simulations are used to illustrate the effectiveness of the proposed control approach.