New approaches to finite-time stability and stabilization for nonlinear system

This paper is concerned with the problems of finite-time stability (FTS) and finite-time stabilization for both continuous and discrete nonlinear systems, which can be represented by affine fuzzy system. Some new FTS conditions are provided and applied to the design problem of finite-time fuzzy regulators. The common Lyapunov function (CLF) approach is first used to analyze the FTS of affine fuzzy system. Then, a piecewise Lyapunov function (PLF), which is less conservative than CLF, is adopted to analyze the FTS of affine fuzzy systems and design corresponding finite-time fuzzy controller. In analysis, the FTS conditions are formulated in terms of linear matrix inequalities (LMIs). In synthesis, the conditions of finite-time stabilization turn out to be in the formulation of nonconvex matrix inequalities for discrete affine fuzzy system (DAFS) and bilinear matrix inequalities (BMIs) for continuous affine fuzzy system (CAFS). Thus, iterative LMI (ILMI) approach is applied to obtain the feasible solutions. Two examples are provided to illustrate the validity of the proposed results.