Analysis Of A Class Of Delta Operator Systems Subject To Actuator Saturation

Saturation nonlinearity widely exists in a variety of practical control systems, but when we design a control system, we always ignore the effect of saturation nonlinearity on the static properties of control systems, and treat the nonlinear systems as linear systems. In the practical production, we have to face the effect of actuator saturation, when the input is larger than the superior limit of actuator saturation, the system will be working in the saturation state, enlarging the input amplitude will not lead to a steady increase of output, on the contary, which may lead to the loss of stability. There are a lot of research productions about the control systems with actuator saturation now, but the analysis about the effect of actuator in delta operator systems and Networked Control Systems(NCS) are not familiar.This paper mainly analyzes the stability and stabilization of the Delta operator systems with actuator saturation, and the stability of NCSs with actuator saturation. When we analyse the effect of actuator saturation, we find that these systems are always local stability, and the stability region can not be expressed analytically, so this paper mainly based on the direct Lyapunov method, and combined the Linear Matrix Inequalities(LMI), by the means of level set of Lyapunov function to estimate the stability region. Our results are given as follows:Firstly, for the Delta operator systems with actuator saturation under linear state feedback controller, we have designed the feedback gain matrix to maximize the local stability region. Utilizing the Lyapunov stability method, we have derived the sufficient theory of local stability for this class of systems by setting quadratic Lyapunov function. Using Matrix theories, we have got the method of estimating the stability region, called as domain of attraction.Secondly, based on the above research, we have introduced a new method which is called saturation dependent Lyapunov function into analyzing the stability of the Delta operator systems with actuator saturation, and improved the above result using this method. We have also summarized the problem of estimate the domain of attraction as an optimization problem, ultilizing the matrix inequality theory. In the end, we have used Matlab numerical simulation to illustrate the effectiveness of the theory.Thirdly, considering the periodic time-varying Delta operator systems with actuator saturation, by setting peiodic time-varying Lyapunov function, we have obtained the sufficient conditions of local stability. By matrix theory we have obtained the method of estimate the domain of attraction. Furthermore, by constructing the augmented system of the original system, we have given the conditions under which the original system is global asymptotic stability. In the end, we have used Matlab numerical simulation to illustrate the effectiveness.In the of the paper, considering the problem of time delay and packet dropout in NCSs, we have taken into account time delay, packet dropout and actuator saturation, and obtained the conditions of local stability. In the end, we have used Matlab numerical simulation to illustrate the effectiveness.