Stability Analysis And Controller Design For Some Classes Of Uncertainty Nonlinear Systems

The stability analysis and controller design for uncertainty nonlinear systems are very important areas in nonlinear control theory.This thesis has investigated respectively that the problems of stability analysis for a class of uncertain system with time-delay,the asymptotic stability of a class of singularly perturbed systems with multiple time delays and the problem of robust stability of singularly perturbed systems with nonlinear uncertainties.The main research results are given as follows:Firstly,the problem of reliable controller design by robust output feedback is investigated for a class of uncertain system with time-delay.The system under consideration involves state time delay and parameter uncertainties.A reliable controller is designed such that the closed-loop system remains asymptotically stable for all admissible uncertainties independently of the time-delay,not only when the system is operating properly,but also when there exist a simultaneous presence of actuator and sensor failures.Secondly,the asymptotic stability of a class of singularly perturbed systems with multiple time delays is investigated.The feedback controls for the slow subsystem and the fast subsystem have been separately designed by frequency-domain stability criteria.Furthermore,a stabilizing composite feedback control has been proposed to guarantee the asymptotic stability of the singularly perturbed systems with multiple time delays.A stability boundε~* of singular perturbation parameterεhas been derived such that the original system under the composite feedback control is asymptotically stable for allε∈(0,ε~*).Finally,the problem of robust stability of singularly perturbed systems with nonlinear uncertainties is concerned.Via introducing state transformation and constructing the Lyapunov function,a stability boundε~* is derived and a sufficient condition which guarantees the singularly perturbed systems asymptotically stable is presented.An example is illustrated to show how to apply the proposed results.