Finite-time H_∞ Control of Cascade Nonlinear Switched Systems under State-dependent Switching

In this paper, we investigate the finite-time H_∞ control problem for the class of cascade nonlinear switched systems consisting of two parts which are also switched systems using a state-dependent switching method. The state feedback controller and the switching law are designed respectively, which guarantees that the corresponding closed-loop system is finite-time bounded and has a prescribed H_∞ performance index; the corresponding sliding motion problems are also considered. Sufficient conditions for the solvability of the problem are obtained. A numerical example is given to demonstrate the validity of the proposed approach.