Robust L₁ Performance Analysis And Synthesis For Switched LPV Systems

In the practical industrial process, we can not achieve the required control effect simply by the approach of dealing with continuous systems or discrete systems. To solve this problem,the concept of hybrid systems is proposed. Hybrid systems are composed of continuous dynamics part and discrete event dynamics part, however, as a special branch of hybrid systems, switched systems have received extensive attention. To put it simply, switched systems are consisted of a series of subsystems described by differential equations or difference equations, and the associated switching signal that specifies the switching among them. At the present stage, the study on switched linear systems is relatively sufficient, but the nonlinear characteristic and time delay characteristic usually existed are of great influence to the systems stability. So the study on switched LPV systems with time-varying delays is very practical and meaningful. For switched LPV systems, this paper investigates the robust control and filtering problem under synchronous and asynchronous case, and the robust model reduction problem. The main results as follows:Firstly, the robust L1 full-order and fixed-order filtering for switched LPV systems under synchronous switching is investigated. Based on the ADT approach, the delay-dependent and parameter-dependent L1 performance criterion is established. As there exist coupling between the Lyapunov parameter matrix and the system matrices, a slack matrix is introduced to decouple it, then a new theorem is obtained which is easier to solve. The robust L1 controllers are also designed to guarantee that the closed-loop systems are exponentially stable and have an L1 attenuation level, and the sufficient conditions of the existing robust L1 controllers are given. As the conditions obtained are PLMIs, we can transform the infinite dimensional PLMIs to the finite dimensional LMIs by approximate basis function and gridding technique,so we can get the feasible solution of LMIs.Secondly, the robust H∞ full-order and fixed-order filter design problems for switched LPV systems under asynchronous switching are investigated, where we assume that the switching instants of the filters lag behind those of the systems. Based on the MDADT approach and Lyapunov stability method, the parameter-dependent H∞ performance criterion under asynchronous switching is established. And the sufficient conditions of the existing robust H∞ filters are given, such that the filtering error systems are exponentially stable with an H∞ performance. Similar to the full-order filters, the sufficient conditions for the fixed-order filters are obtained, and can be transformed to the solution of convex optimization problem.Finally, the robust L1 model reduction for switched LPV systems is investigated by convex linearization approach. The objective is to find a reduced model to approximate the original high-order system under an arbitrary switching signal with ADT constraint, such thatthe error system between the two systems above is exponentially stable and have an L1 disturbance attenuation level of the error system.