Feedback control for a class of lipschitz nonlinear systems

The design of state feedback controllers and dynamic output feedback controllers is given for a class of Lipschitz nonlinear systems. We transform the nonlinear systems into linear parameater varying (LPV) systems by the use of the differential mean value theorem (DMVT). A sufficient condition is provided by using linear matrix inequalities (LMIs) and the state feedback controllers and dynamic output feedback controllers are gained. When the feedback control laws are applied to the systems, the closed-loop systems are globally asymptotically stable. A simulation example shows the feasibility and effectiveness of the conclusion.