Analysis Of Stability And L₂-performence For Systems Subject To Actuator Saturation

In this paper, both stability analysis and L2-performance analysis for system subject to actuator saturation are discussed. For any system, stability is quite critical among all research questions and stability is not an exception for saturated systems. The L2-performance analysis has also an important influence on systems subject to actuator saturation and disturbance. Both of the above problems are studied in this paper. The present paper is organized as follows:First, the problem of stability for single input discrete time delay systems subject to actuator saturation is studied. Under a certain assumption, the sufficient conditions which identify whether the system is of global asymptotic stability(GAS) or regional asymptotic stability(RAS) are presented. These conditions are described by a group of linear matrix inequalities(LMIs) and the minimum eigenvalue of the matrix. Then, based on the conditions, the methods for the domain of invariant attractive of the systems are designed. Finally, the feasibility of the obtained condition is illustrated by an example.Second, the problems of asymptotic stability of multiple-input continuous systems are studied. The single input continuous saturated system and the single input continuous delay saturated system are extended to the multiple input continuous saturated system and the multiple input continuous delay saturated system. The direct expressions of the saturate controller are given. The sufficient conditions of global asymptotic stability and regional asymptotic stability are prented by the Lyapunov method. In addition, the conditions which identify whether the multiple-input delay continuous system is the delay-dependent asymptotic stability are presented. These conditions are described by a group of linear matrix inequalities. Then, the domain of invariant attractive of the systems is given. Finally, the effectiveness of the proposed conditions is demonstrated by a numerical example. Third, the problems of L2-performance analysis for uncertain continuous systems and discrete-time systems are studied. Using linear matrix inequality method and Schur lemma, two ellipsoid domains where the smaller one is included in the bigger one are designed. Above all, when disturbance exists, trajectories of the closed-loop system from the smaller ellipsoid domains can also remain in another ellipsoid domain. And the corresponding closed-loop saturating system is finite gain L2-stable. In addition, when the disturbance does not exist, the corresponding closed-loop system is robust internal stability. And the bigger ellipsoid domain is included in the basin of attraction of the closed-loop system, and it is contractive.