Stability Analysis And Synthesis Of Control Systems With State Saturation

Saturation nonlinearities are ubiquitous in engineering control system. Whensaturation occurs, whether the system has good stability is one of the research hot spotin control field. In this paper, the main content is the stability analysis of controlsystems with state saturation. It includes the problems of stability analysis andcontroller design in the discrete time system with saturating state, continuous timesystem with partial state saturation and time-delay systems with state saturation.Moreover, it takes advantage of the method of the convex combination to deal withsaturated and utilizes Lyapunov theory to judge the stability of the system, and designthe state feedback controller of the system.Firstly, it briefly introduces the development of saturation system, the researchstatus on state saturation system and the main contents of this paper. It gives theconcept and mathematical description of control systems with state saturation,method of dealing with the saturated part, stability theory of control systems andmathematical lemmas.Secondly, the stability of linear systems with state saturation in this dissertation isdiscussed. By means of a proper additional matrix, using Lyapunov theory andsaturated function definition, it gives the sufficient condition which guarantees theclosed-loop systems is asymptotic stabilization in the large at the origin and providesthe design procedures of the controller. At last, the numerical results and simulationexamples are given.Thirdly, in allusion to the partial state saturation system with uncertainties and theuncertainties are norm bounded, it researches the stability conditions and the designmethod of controller and constraints the system states in a unit of a polyhedron. Usingthe method of convex combination and the stability theory of Lyapunov, the sufficientcondition which the system with partial state saturation is globally asymptoticallystable at the origin is obtaine d. Then design method of the state feedback controllerand the numerical examples are obtained.At last, the stability problem of the delay control systems with state saturation isconsidered, using the free weighting matrices, all the derivative of theLyapunov-Krasovskii functional are merged into an integrator. Utilizing the method of convex combination and stability theory of Lyapunov, the sufficient conditionwhich the system with partial state saturation is globally asymptotically stable at theorigin is obtained.