Stability Analysis And Controller Design For A Class Of Nonlinear Systems

The stability analysis and the controller design of nonlinear systems are very important areas in nonlinear control theory. Recently years, the investigators have especially paid attention on the research of nonlinear uncertain systems and feedback linearizable systems, and some achievements have been obtained.This thesis has investigated respectively that the problems of the output feedback global exponential stabilization for a class of nonlinear uncertain systems, the global stabilization for a class of nonlinear systems and the switching controller design for a class of feedback linearizable systems. In the first captain, the developing background and the present researching situation of the nonlinear systems' theory have been introduced. In the second captain, some basal theorems interrelated with this thesis have been introduced. And in the third, the fourth, the fifth captain, the controller design and the stability analysis of nonlinear systems have been studied in detail. The main research results are given as follows:The first, the problem of global exponential stabilization for a class of nonlinear uncertain systems is considered. We have extended the idea for output feedback controller design of the single-input single-output systems to the Multi-input Multi-output nonlinear systems. According to the systems' structural performance, a design method of output feedback control law for the nonlinear uncertain systems is presented. We design the Lyapunov function and the output feedback control law, which globally exponentially stabilize the nonlinear uncertain systems. A new sufficient condition is presented for the class of nonlinear uncertain systems to be globally exponentially stable.The second, the problem of global stabilization for a class of nonlinear systems is considered. According to the characters of the systems, the feedback control law is designed and the global asymptotic stabilization of the closed-loop systems is proved using the Lyapunov's second method. And we extend the results to more generalized situation, which makes the research results more applied range.Finally, the switching adaptive controller for a class of feedback linearizablesystems has been studied. We have proposed the switching adaptive control law for the systems and designed the Lyapunov function in this thesis. It is proved that the proposed switching adaptive control law guarantees the solutions of the nonlinear systems boundedness and convergence of the tracking error to a residual set based on the Lyapunov's stability theory. The residual set can be made arbitrarily small by choosing a certain design parameters.