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Finite-time stability and stabilization for a class of nonlinear discrete-time singular switched systems

In this paper, the problem of finite-time stability analysis and state feedback stabilization for a class of nonlinear discrete-time singular switched systems is discussed. First, based on the switching Lyapunov theory and the implicit function theorem, a sufficient condition is developed in the form of linear matrix inequalities (LMIs) which guarantees that the nonlinear discrete-time singular switched system is regular, causal, has a unique solution in a neighborhood of the equilibrium point, and is finite-time stable. Then based on the above condition, a condition on the existence of the finite-time state feedback stabilization controller for the nonlinear discrete-time singular switched system is proposed and the design method is given. Finally, two numerical examples are given to show the effectiveness and correctness of the proposed methods.