Dissipativity of stochastic nonlinear control systems with state-dependent switching

Dissipativity of stochastic nonlinear control systems with state-dependent switching is investigated in this paper. Under the assumption that the active regions of subsystems are overlapped, a switching law can be constructed. Meanwhile, by the aid of Itό´s formula, the corresponding local solution of switched system is generated. Based on stochastic dissipativity and stochastic Barbalat lemma, the criteria on dissipativity and stability of switched system are presented by using Lyapunov function method. As a case research, for a family of cascaded systems, a switching law can be designed such that the cascaded switched system is dissipative.