The Study Of Robust Stability For Classes Of Uncertain Systems With Multiple Delays

Uncertainties and time delays widely exist in a variety of practical systems, and they areimportant factors that lead to the system instability and the declination of dynamicperformance. Most systems have several time delays, and by taking full account of theinfluence of uncertainties and time delays on the control effect of the system, the researches ofthe robust stability of uncertain system with multiple delays, whether in theory or practicalapplication, are of great significance.Based on the Lyapunov stability theory, Lyapunov-Krasovskii stability theory, robuststability theory, Riccati equation method and linear matrix inequalities method(LMI), therobust stability is researched of uncertain systems with multiple delays in the paper, and thedesign method of the robust controller and the robust stability conditions are provided for thetwo different uncertain systems with multiple delays.The main contents consist of several parts as follows.In chapter I, the basic concepts and research status are summarized for the uncertaintime-delay systems and the uncertain neutral system with time delay, and some problems to besolved are summarized in this paper.In chapter II, the object of study on robust control and some uncertainty control systemmodel is introduced, linear matrix inequality and stability theory is given in to related lemmato be used in the paper.In chapter III, the robust adaptive control problem is studied for a class of uncertain timedelay system with multiple state and input delays in the paper. Based onLyapunov-Krasovskii functional, an adaptive state feedback controller without memory isdesigned, and in certain conditions, this controller can make the closed-loop system ultimately uniformly bounded, the result is proved. Finally, a numerical example provided to illustrate thefesability of this method, and the shortage of the Riccati equation method is adoption also isexplained in the paper.In chapter IV, the delay-dependent robust stability is studied for the neutral type systemswith time-varying uncertain coefficients and discrete multiple delays. Based on linear matrixinequality technic, a simplified method is proposed to calculate the free weighing matrices andthe upper bounds on the delays for the system. Both neutral delays and discrete delays areconsidered in the system and the sufficient conditions for the stability and robust stability ofthe system are obtained. Finally, the feasibility of this method is illustrated by giving anumerical example, and this method is conservative in some aspect is pointed out.