Switching Law Of The Switching Systems And Its Input U(t) The Best Overall Design Method

Switching systems is a special system composed of a limited number of subsystems or dynamic model,and the essential difference with other systems is it has a switching rule.When choosing an appropriate switching rule,the switching system can be made stable from unstable to optimal performance.Therefore,the switching system is not only of great significance in theoretical research,but also in practice has been widely used.This paper obtains the following four aspects of innovative research results:(1)The general conditions for the extreme conditions of the abstract performance index optimization problem are generalized.We obtained the existence theorem of the first order variation functions of the new functional of the abstract multivariate functional and operator complex and a necessary condition for first order variational expressions and their functional extremums.A generalized processing is done for the linear and nonlinear switching systems,the result is a general theoretical basis for the input design scheme when the switching system achieves the optimum performance.(2)For a kind of functional in the form of integrals,we obtain a necessary condition for obtaining the extremum under the extreme conditions of system conditions described by differential equations.(3)The controller and switching rule of linear switching system under the optimal quadratic performance index are studied.Get several kinds of corresponding optimal controller design method,and use the optimal controller to get an optimal switching rule.However,since there are an infinite number of controllers,the future is devoted to designing a limited number of controllers and switching rules with limited switching times.(4)Design of controller and switching rules for a class of switched systems with uncertainties and time-varying delays.The Lyapunov function,convex combination technique and linear matrix inequality are used to give design scheme of the switching rules for the system satisfying the robust H_?performance and give a matrix inequality about controller.