Stability Analysis Of Discrete-time Systems With Nested Actuator Saturation

Saturation is a common, and actuator saturation is one of the most common and most important saturation nonlinearity, we have always been more concerned about how to determine its stability, for this point has a large number of literature for its analysis and explanation. This article is mainly for multi-saturation phenomenon (i.e., the nested saturation) for analysis, saturation is always from the inside to the outside of the saturated saturation occurs sequentially. In this thesis, the convex combination method was adopted to saturated linearization, at the same time introducing a Lyapunov function, using the system invariant set to estimate the domain of attraction, then transfer the domain of attraction problem into a class of constrained optimization problem, and finally, it can be solved using MATLAB.The third chapter of this thesis mainly discusses the discrete-time systems with nested actuator saturation. It analyzed the given system's stability without external disturbance and outside disturbance. Firstly, I dealt the nested actuator saturation with the method of convex combination. Then I used Lyapunov stability theory to construct the corresponding shrinkage invariant set for ensuring the stability of the system, and designed a controller. Finally this thesis has carried on the preliminary estimate on the attraction domain of the given system using LMI theory. Theorem in this thesis is verified by numerical simulation and the controller is effective and feasible.The fourth chapter of this thesis respectively using the quadratic Lyapunov function and saturated associated Lyapunov function for uncertain discrete-time systems with nested actuator saturation to analyze the stability. Using Finsler's lemma, the theorem for guaranteeing system stable is obtained. The controller is respectively designed for the above two methods, and the theory of LMI is applied to obtained the given system's attract domain estimation.