Disturbance Rejection Research Of Actuator Saturation System Based On Complex Quadratic Lyapunov Function

Actuator saturation, as a common and typical nonlinear constraint, is oftenencountered in practical control systems and has a significant impact on the stabilityof the system. The related research have received considerable attention and hassignificance in theory and reality. This paper is concerned with two aspects ofactuator saturation system by using complex quadratic Lyapunov function:1. The disturbance rejection problems are researched for linear systems withactuator saturation and external disturbances. Firstly, by applying the lineardifferential inclusion method, the saturation can be converted into a linear form,based on constructing a supplementary matrix H. Therefore, the approach ofprocessing saturated nonlinear has less conservative than the existed results.Secondly, by using the complex quadratic Lyapunov function method, a newinvariant set condition is obtained in the linear feedback control and an optimizationmethod of the estimation of attraction domain is obtained. The optimization methodexpands the estimation of attraction domain and achieves disturbance rejection ofthe system. Finally, the estimation of attraction domain is converted into anoptimization problem with LMI constrains. By using LMI toolbox in Matlab, anumerical example is shown to illustrate the effectiveness of the method.2. The disturbance rejection problems are researched for actuator saturationlinear systems with external disturbances and uncertainty. The uncertainty is allowedto be unconstructed uncertainty and norm bounded uncertainty respectively. Firstly,by using some known lemmas, the saturated nonlinear can be processed andobtained a intensified upper bound. Secondly, by applying Lyapunov functionmethod, an invariant set condition of the systems are given. Further, combing theabove invariant set condition and applying the complex quadratic Lyapunov functionmethod, a new invariant set condition and disturbance rejection method are obtained.Finally, for estimating the domain of attraction, an optimization method is designed for the close-loop system. A numerical example is shown to illustrate theeffectiveness of the invariant set conditions and the optimize method.Motivated by the above discussions, it can be easily seen that the complexquadratic Lyapunov function method is very effective in terms of expanding theestimation of domain attraction.