Finite Frequency H∞ Control For Linear Singular Systems

Singular systems can not only describe the dynamic relationship between variables,but also describe the algebraic constraints between variables.Compared to normal state space systems,they represent actual systems more naturally.This has made singular systems a hot topic of research ever since they were proposed.In practical control systems,each link often has specific frequency domain response characteristics,so researchers have different requirements for system performance in different frequency ranges.This makes it necessary to conduct finite frequency performance analysis of the system.At present,many achievements have been achieved in the study of finite frequency problems for singular systems.However,many of these achievements focus on fault detection,fault estimation,or filtering,while research on finite frequency control for singular systems has not been reported yet.Therefore,the research in this article is more innovative.Based on the generalized Kalman Yakubovic Popov lemma,this paper discusses and analyzes the finite frequency performance of singular systems,and obtains corresponding finite frequency controllers through several strict sets of linear matrix inequalities.Specifically,it includes the following three aspects:Firstly,for general linear singular systems,this paper proposes two new finite frequency analysis theorems from the perspective of frequency domain.This theorem can be seen as a generalization of the generalized Kalman-Yakubovic-Popov lemma in singular systems.Based on these theorems,two state feedback H∞ controllers and a full information feedback H∞ controller are designed.Then,a simulation case is used to illustrate the effectiveness and superiority of the proposed method.Secondly,based on the finite frequency analysis theorem for singular systems,this paper further extends the finite frequency performance analysis idea to nonlinear singular systems,and designs a state feedback H∞ controller and a static feedback H∞ controller.Then,the feasibility of the existence of a finite frequency controller is verified through a simulation case.Finally,for singular time-delay systems,this paper proposes three finite frequency bounded real lemmas from the perspective of frequency domain and time domain.Using this lemma,this paper analyzes the finite frequency performance of singular time-delay systems,and designs two state feedback H∞ controllers and a static feedback H∞ controller.The feasibility of the finite frequency controller is verified through simulation experiments.This article comprehensively summarizes and deduces the problems of finite frequency control for singular systems,providing different ideas for the design of various finite frequency controllers in the future.