Delay-dependent condition for absolute stability of Lurie control systems with multiple time delays and nonlinearities

The absolute stability of Lurie system with multiple time delays and nonlinearities is considered in this paper. Based on the Lyapunov stability theory, using the descriptor system approach and the method of decomposing matrices, a novel delay-dependent sufficient condition for the absolute stability of Lurie system is derived and expressed in the form of the linear matrix inequality (LMI). The maximum upper bound of the allowable delay is obtained by solving a convex optimization problem. A numerical example shows that the result obtained in this paper improved the estimate of the stability limit over some existing results.