Stability Analysis For Continuous-time Systems With State Saturation In Different Restricted Areas

In control systems, the saturation factors have a serious effect on systemperformance, and even cause instability. Therefore, the study about the stabilit yfor control systems with saturation is necessary, and has important practicalsignificance. Through the judgment of the existence of equilibrium points andsteady orbital periodic solutions and limit cycles in the restricted area, sufficientconditions for continuous-time linear systems with state saturation to be globallyasymptotically stable are given. The stability for systems with saturation isconsidered in the cube restricted area and in the sphere restricted area.1. The stability of continuous-time three-dimensional control systems withstate saturation is invest igated in the cube restricted area. By considering theequilibrium points of the systems, sufficient conditions are presented for theboundary of the cube restricted area not having an equilibrium point which showsthat the systems only have the origin as equilibrium point. Moreover, sufficientconditions of globally asymptotical stability for the control systems are obtainedbased on Poincare-Bendixson property, the second additive composite matrix andorbitally asymptotic stability of the periodic orbit.2. The stability of continuous-time control systems with state saturation isinvestigated in the disc or sphere restricted area. For the planar systems withstate saturation under disc restricted area, by polar coordinate transformation, asufficient condition for the uniqueness o f the equilibrium po int is obtained. Thenthe condition for the nonexistence of limit cycles is obtained by usingBendixson-Dulac discriminance. Therefore sufficient conditions are given forplanar systems with state saturation to be globally asymptotically stable. For thethree-dimensional systems with state saturation under sphere restricted area, similar to the idea in the case of the cube restricted area, sufficient conditions ofglobally asymptotical stability for the systems are obtained based on thecondition for the uniqueness of the equilibrium point and orbitally asymptoticstability o f the periodic orbit.