Robust H-infinity Control For Uncertain Switched Nonlinear Systems

Switched systems have attracted much attention since its theoretical research hasbecome more sophisticated and widely used in practical problems． The stabilityproblem of switched systems is one of the most popular areas in the present study; onthe other hand, H∞control theory has become one of the important direction in thestudy of modern control theory． It is possible that the results about H∞control fora general are generalized to switched systems． However, compared with the stabilityresults of switched systems, study robust H∞control of uncertain nonlinearswitched systems is still rare． Therefore, we do some work on this aspects,that isrobust H∞control problem for a class of uncertainties nonlinear switched systemsis studied．This article introduces the background of switched systems and robust H∞control． At first, the robust H∞control problem of uncertainties switched systemswith uncertainty appearing input channel,extemal interference and controloutput． With the use of multiple Lyapunov functions, by the design of state feedbackcontroller and switching law, making the closed-loop system is asymptotically stablefor all admissible uncertainties, but it also has a specifiedL2gain． This paper givesa sufficient condition of uncertain switched systems robust H∞control problemwhich is solvable is that a group containing a scalar function of the partial differentialinequality of their respective solvability does not depend on the Hamilton-Jacobiinequality． On this basis, as an application, with the hybrid system state feedbackstrategy, we further study the problem of robust H∞control of uncertain nonlinearsystems of non-switching．Then, we have discuss in a class of nonlinear switchedsystems with non-fragile robust H_∞control problem． When the controllerperturbation and a controlled output contain uncertainties, using multiple Lyapunovfunctions method, switched systems, switched systems for all admissible uncertainties,the corresponding closed-loop system which is asymptotically stable and has a H∞performance． We get sufficient conditions for the existence of non-fragile state feedback controller, and the results do not depend on the Hamilton-Jacobiinequality． As an application, with the help of the hybrid state feedback strategy wediscuss the non-switching uncertain nonlinear systems, non-fragile robust H∞control problem．Finally, the present work is systematically concluded．...