Study On The Stability Of Discrete-time System With Nested Satruation Actuator Based On Lyapunov Function

Nested saturation, as a common nonlinear constraint in the practicalengineering domain, affects the performance of control systems even leads to theinstability of systems. Switching system being a dynamic system is used toaccurately describe the physical phenomena of switching characteristics. In recentyears, the switched system has obtained more and more attention owing to its simplestructure and extensive applications. Therefore, it is of important significance ontheoretical research and practical application to study switched system with actuatornested saturation. In this paper, the item of nested saturation is properly processed,and then the problems of stability analysis and controller design are proposed for thetwo classes of discrete switched system by applying Lyapunov stability theory.1. The stability analysis for discrete systems with actuator nested saturation isdiscussed. Then the item of nested saturation is converted into convex combinationby a derivation approach from the inside to outside. Further a sufficient condition ispresented to guarantee the global asymptotical stability of the addressed system byintroducing Lyapunov function.2. The disturbance rejection problem is considered for discrete switchedsystems with actuator nested saturation and external disturbances of L2-normbounded. The addressed system is converted into linear results and the anti-windupfeedback controller is designed by using the method above. Then, sufficientconditions of the stability analysis for the addressed system are proposed byconstructing appropriate Lyapunov function. Further it is proved that the statetrajectories from the origin are retained within the bounded collection. Finally, anumerical example is given to verify the feasibility and effectiveness of the results.