Switched Controllers Design And Performance Optimization Of Linear Systems

In engineering practice,it often happens that using a controller can not achieve the ideal control effect.However,switching between multiple controllers can often improve the control effect.Designing several alternative controllers and a switching rule among multiple different controllers,so that the controlled systems can achieve asymptotic stability or meet other corresponding performance indicators,have important significance for practical engineering applications.In this thesis,the following innovative findings can be obtained in switched control:(1)By analyzing the existence of the stability switched controllers for linear systems,a sufficient condition for the asymptotic stability of n-dimensional linear time-invariant continuous system with switched control is obtained,and the design method of switched controllers and the corresponding switching rule is given under this condition.Finally,a numerical example is given to verify the feasibility of this method.The proposed controllers have better performance than the conventional controller.Furthermore,several properties are obtained of linear system with this type of controllers.(2)When a single controller can not make the system asymptotic stability,this thesis preliminarily studies whether the system can be asymptotic stability by doing switched control.For two-dimensional linear time-invariant continuous system,it can be concluded that if a single controller can not make it stable,then switched control also can not make it stable.In addition,corresponding results for several types of n-dimensional linear time-invariant continuous systems also can be obtained.(3)The design of guaranteed performance for n-dimensional linear time-invariant continuous system with switched controllers is studied.Based on public-Lyapunov function technique and multiple-Lyapunov function technique,by combining the convex combinatorial technique and the linear matrix inequalities,two kinds of switched controllers with guaranteed performance for the system and design schemes for switching rules are obtained.