Finite-time stability of switched stochastic systems with incremental quadratic constraints

The main purpose of this paper is to study the stability problem of switched systems with incremental quadratic constraints. Compared with the switched systems with Lipschitz condition, the nonlinear switching system discussed in this paper are more general. Based on the mode-dependent Lyapunov function and the linear matrix inequalities method, the sufficient conditions of the stability in probability and finite-time stability of nonlinear switched systems with incremental quadratic constraints are derived. In our main results, the conditions on LV are relaxed and the coefficients can be positive or negative, so the subsystem may be stable or unstable, respectively. Finally, we give a specific example to show the effectiveness of our results.