Stability Analysis And Synthesis Of Control Linear Systems With Saturation

The physical constraint usually exists in daily life and all kinds of engineeringfields. One of the most common phenomenons is the saturation. In the control system,the nonlinear saturation will seriously affect the system performance index. Therefore,the research on saturation system has attracted attention in recent years.The saturation system consists of state saturation, input saturation, outputsaturation and multiple variables saturation. This study focuses on control systemstability of input saturation and state saturation. The main contents of the study are:stability of input saturation control system with constant and varying time delay andthe design method of the controller; stability of input saturation control system withmultiple time delaying and the estimation problem of attraction domain; studies theproblem of a large range of global asymptotic stability of full state saturation system.This study mainly applies methods of sector region and convex combination todispose saturation. Based on Lyapunov stability theory, this paper obtains the systemstability criterion, and makes a solution by using LMI toolbox.The study includes contents of following aspects concretely:Firstly, the study makes a brief introduction of the background of saturationcontrol system, the significance of the research, present researches at home andabroad and its main contents. Besides, several methods of saturation treatment andbasic concepts and lemmas are also introduced.Secondly, the study explores the stability of the input saturation system withconstant and varying time delay, and uses the sector region method to disposesaturation. According to the definition of the Lyapunov stability theory, the study getsthe stability criterion and gives the design method of the controller.Thirdly, the study focuses on the stability of the input saturation system withmultiple time delays. On the basis of Lyapunov stability principle, the study disposessaturation with the method of convex combination, changes the nonlinear system intoa linear system and obtains sufficient conditions of asymptotic stability of the system.With the help of polyhedron and ellipsoid reference set, this paper estimates attractiondomain size of the system, and solves this problem by using MATLAB toolbox.Fourthly, the study makes an inquiry of the stability of full state saturation and itdisposes saturation with the method of convex combination. Based on the theory ofLyapunov, the study gives the system stability criterion of global asymptotic stabilityof the state saturation control system and the design method of the controller. Finally, a numerical example is given whereby to find little conservation of results.Finally, a summary and outlook of the study is given.