Study On Robust H_∞Guaranteed Cost Control For Nonlinear Singular Systems

In many practical matters such as engineering, national world, human society, Thenonlinear singular system is one of the most representative and universal control system.Such as space systems, economic systems, ecosystems, which are nonlinear singularsystems in nature. In theory, the robust H-infinity guaranteed cost control guarantees theminimum of energy consumption and impregnability of quality of this control system,when uncertainties have been changed in a scale. We get the best results under the currentsituation. The robust H-infinity guaranteed cost control problem is to the hot issues ofcommon concern for nonlinear singular system control.This article thoroughly studied robust H-infinity guaranteed cost control problem ofnonlinear singular systems. The main work as followings:First this paper discusses the issue of robust H-infinity guaranteed cost controlproblem for a class of uncertain singular systems with mixed time-varying and nonlinearperturbation. For this nonlinear uncertain singular systems with time-varying whichuncertain parameters satisfying some conditions and nonlinear disturbance meet linearconstraints, the aims are to design a robust controller and a robust H-infinity guaranteedcontroller, respectively, to the closed-loop system is asymptotically stable and meetH-infinity performance. By means of the linear matrix inequality approach, sufficientconditions for existence of robust H-infinity controller and robust H-infinity guaranteedcost controller are presented. A numerical simulation proves the validity of theconclusions.Next robust H-infinity guaranteed cost control for a class of uncertain discretesingular systems with mixed multi-time delay and nonlinear perturbation was studied. Inthe system, the nonlinear perturbation satisfying some constrained in the Lyapunovfunction and linear matrix inequality. This uncertainty is a function of time and state. Asufficient condition for the existence of robust H-infinity guaranteed cost controller wasgiven by linear matrix inequality approach. The simulation results show that the controlleris correct and the scheme is availability. And ensure that the closed-loop system isasymptotically stable.Then robust H-infinity guaranteed cost control for the other class of uncertainsingular systems with mixed multi-time delay and nonlinear perturbation was discussed. Asufficient condition for the existence of robust H-infinity guaranteed cost controller was given by linear matrix inequality approach based on Lyapunov stability theory and linearmatrix inequality method. The closed-loop system is asymptotically stable and make it didnot exceed get the minima upper bound of performance cost. The simulation resultsprovided the method in this paper is very practical.The last part summarizes the key points of this paper and expectation of robustH-infinity guaranteed cost control problem of nonlinear systems.