Asymptotic stability and stabilization for a class of nonlinear descriptor systems with delay

Abstract

This paper discusses asymptotic stability and stabilization for a class of nonlinear descriptor systems with delay. The nonlinearity of the system is a continuous function of the time and system state, and the Jacobi matrix of the function is norm-bounded. A sufficient condition for the existence and uniqueness of the solution to the descriptor system is proposed by a linear matrix inequality (LMI) approach. Under the condition, using nonlinear methods, the asymptotic stability for the system is obtained. In addition, to stabilize the descriptor system, a parameterized representation of the state feedback controller is given in terms of a solution to an LMI. Finally, the effectiveness of the approach is illustrated by numerical examples. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society