Practical stabilisation of discrete-time switched nonlinear systems without a common equilibrium and using hybrid switching functions

Abstract

This paper presents a new practical stabilization method for discrete-time switched nonlinear systems without a common equilibrium point among all modes. The proposed method has two main features. First, the number of nonlinear terms in the stability conditions is independent of the number of switched system modes. The result is that the computational cost is reduced, and it can be applied to switched systems with a large number of subsystems. Second, using switched Lyapunov functions, hybrid switching laws are designed to preserve the practical stability property in both the closed-loop state-dependent switching function and the open-loop time-dependent one. As a result, when the state data is lost during sensor or communication failures, the controller can change the control scheme from a closed-loop state-dependent switching function to an open-loop time-dependent one without loss of stability property. Numerical examples are presented to illustrate the validity and efficiency of the proposed method.