H_∞ Control Of System With State Saturation

System with state saturation is common, in the practical system, there are many unpredictable interference effects on the performance of the system. Saturation limit,time-delay and uncertainty factors will affect the stability of the system in the practical engineering problems. Some control schemes ignore the factors and become difficult to apply to the actual engineering. In order to solve the stability problem for state saturation system, the paper studies the H_∞ control.This paper focuses on H_∞ control of uncertain continuous system with state saturation, time-delay continuous system with state saturation and uncertain discrete-time system with time-delay and state saturation. According to the convex combination method the saturation item is dealt with, uncertain terms satisfy norm bounded, the new criterion of the stability of the system is given and the state feedback controller based on the H_∞ control theory is designed. An example is given and solved by the LMI toolbox in MATLAB.The content of this paper is mainly composed of the following aspects.Firstly, the paper makes a brief introduction to the research background,significance of saturation system and H_∞ control as well as the research status,introduces some basic concepts and lemma about this paper.Secondly, we research H_∞ control of uncertain continuous system with state saturation. The saturation item of the system is represented by convex combination,the sufficient conditions for the stability of the system with a certain degree of attenuation is obtained, the sufficient condition is further converted to linear matrix inequalities which can be solved by linear matrix inequality method, and the state feedback controller which makes the system stable is also designed.Thirdly, the thesis studies H_∞ control of time-delay continuous system with state saturation. The saturation item of the system is expressed by convex combination,under the constraint of performance index, the Lyapunov function is introduced, and the sufficient conditions for the stability of the system are given. According to the Schur lemma, the results are expressed in linear matrix inequalities, a state feedbackcontroller for the system is proposed.Fourthly, the paper considers about H_∞ control of uncertain discrete-time system with time-delay and state saturation. In the part the saturation item is expressed as a convex combination. Then it is further processed with inequality scaling, which makes the system be converted to a linear systems. We design a state feedback controller for the system. By using the properties of the matrix of inequality and introducing positive definite matrix, the new criterion for stability of the discrete-time systems with time-delays and state saturation is obtained by Lyapunov method.Finally, the full text is summarized, and the future research work is prospected.