| As the nonlinear constraints in the control systems, state saturation appears inmany practical systems, and has an important impact on the stability of the systems.The related research has been subject to extensive attention of scholars. It not onlyhas significance in practical application the stability study of state saturation systems,but also has certain challenge in theoretical research. This thesis focuses on twoaspects of the state saturation control systems.1. If state saturation function is h(), the stability of uncertain continuous linearsystem with state saturation is studied, The stability conditions for the full statesaturation system and partial state saturation system are discussed respectively.Under the hypothesis that the uncertainties have convex polyhedron structure, useimproved convex domain method to express the state saturated function as a convexcombination of the linear functions, and a sufficient criterion of the systems globallyasymptotical stability at the equilibrium point is given by applying Lyapunovmethod. The linear matrix inequality (LMI) representation of the criterion ispresented. An iterative algorithm is designed to determine globally asymptoticalstability of system at the equilibrium point. The validity of the iterative algorithm isverified by numerical examples.2. If state saturation function is (), the globally asymptotical stability of theequilibrium point for the there-dimensional continuous state saturation system isstudied. Similar to the idea of two-dimensional continuous state saturation system,by proving boundedness of state trajectories and nonexistence of closed trajectoriesfor three-dimensional system, a sufficient condition is obtained for determineglobally asymptotical stability of three-dimensional continuous state saturationsystem at the equilibrium point, which extended the globally asymptotical stabilitycriterion of the equilibrium point for two-dimensional system to there-dimensionalsystem. |
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