Practical stability of a nonlinear system with delayed control input

Abstract

The problem of delayed input control for a nonlinear system is discussed, where the nonlinearities of nonlinear systems are not assumed as Lipschitz continuous, they can be non-Lipschitz continuous or discontinuous in this paper. Notice that as a general nonlinear system, its sub-systems may have no common equilibrium or no equilibriums, but their trajectories may still be kept near equilibriums. Motivated by this, practical stability of nonlinear systems is considered by employing the Lyapuov method. Practical stability criteria in forms of linear matrix inequalities are obtained, where improved integral inequalities are given to reduce the conservatism of the obtained results. Finally, the obtained results are applied to analyze two problems of load frequency control of a one-area networked power system with sampled input and flight control of a two-degree-freedom helicopter system. The advantage and effectiveness of our approach are shown by a comparison with the literature.