Stability analysis for a class of switched nonlinear systems

This paper addresses the stability analysis of a class of switched nonlinear systems. The switched systems have uncertain nonlinear functions constrained in a sector set, which are called admissible sector nonlinearities. A sufficient condition in terms of linear inequalities is presented to guarantee the existence of a common Lyapunov function, and thereby to ensure that the switched system is stable for an arbitrary switching signal and any admissible sector nonlinearities. A constructive algorithm based on the modified Gaussian elimination procedure is given to find the solutions of the linear inequalities. The obtained results are applied to a population model with switchings of parameter values and the conditions of ultimate boundedness of its solutions are investigated. Another example of an automatic control system is considered to demonstrate the effectiveness of the proposed approaches.