Stability Analysis Of Linear Systems With Saturation Control

Saturation is the most commonly encountered nonlinearities in control systems. Saturation nonlinearity is unavoidable in most actuators. When an actuator reaches such an input limit, it is said to be"saturated". Since efforts to further increase the actuator input would not result in any variation in the output, the presence of saturation can debase the performance, even lead the closed-loop system to an unstable behavior. Saturation complicates the problem. It is desired to study on these issues in theory or practice. Therefore it is important to discuss the stability of linear systems with control constraint.First, the problem of stability for multi-input discrete-time systems with control saturation is studied. By defining the multi-input saturation function and based on the Lyapunov method, a criterion which guarantees global asymptotic stability of the system is given. The invariant attraction region of the given system when the criterion is not satisfied is also presented. In addition, an algorithm is provided to perform the result, and an numerical example is given to illustrate the effectiveness of the proposed designing technique.Second, the stability of multi-input discrete-time linear delay systems with control saturation is investigated. Under some assumptions, in view of the case of the actuator with control saturation, based on the Lyapunov method, the sufficient criterion of global asymptotic stability of the systems is given by defining the multi-input saturation function. In addition the description of invariant attraction region is proposed when the presented criterion is unsatisfied. Finally, an algorithm is designed to demonstrate the presented results, and a numerical example illustrates the feasibility and efficiency of the algorithm.Third, the stability for an uncertain discrete-time system with saturation is investigated. Based on the Lyapunov method and by defining the saturation function, the criterion which guarantees the global asymptotic stability of the system is obtained. The invariant attraction region of the given system when the criterion is not satisfied is also presented. In addition, an algorithm is provided to perform the result.Finally, the asymptotic stability of delay linear system and uncertain linear system with control constrain is studied by using Lyapunov stability theory, and the method for testing if the closed loop system is globally asymptotically stable or regional asymptotical stable is presented. In addition, the effectiveness of the approach is demonstrated by examples.