Design Of Robust H_∞Controller For Uncetrain Systems With Time-delay

In the process of industrial production, time-delay phenomenon is widespread. It is thetime-delay that makes the analysis and synthesis become more complex, and even damage thestability and performance indicators of system. In order to meet the requirements for thestability of control system, the scholars constantly research the time-delay systems to obtainbetter methods. So the study of time-delay systems has always been the hot spot of the controltheory. In this article, through constructing suitable Lyapunov function with applying Jenseninequality, delay decomposition method, the method of integral inequality, the time-delaysystem is researched mainly based on H∞control theory to obtain a class of less conservativeH∞controller.First, this paper deals with the design of robust H∞controllers for uncertain lineartime-varying delay systems and uncertain nonlinear singular systems with time-varying delay,by taking new Lyapunov-Krasovskii functions, it obtains the analysis of robust stability aboutdelay-dependent and the design method of robust H∞controllers based on linear matrixinequalities (LMIs). So the closed-loop system is asymptotically stable, and satisfies the givenH∞disturbances rejection level of delay-dependent conditions. Then low conservativememory controllers are designed.Finally, numerical examples are given to illustrate theeffectiveness of the design approach.Second, based on Lyapunov stability theory and LMI method it mainly investigates therobust H∞fault-tolerant control problem of the uncertain linear systems with intervaltime-varying delay. When something goes wrong with actuators, the delay interval will bedivided into two interval. The method will give a reasonable Lyaponov functional in makingfull use of the upper and lower bounds of the time-delay on each interval. The integralinequality approach combined with will also give a sufficient conditions that the time delaysystem which actuators is wrong, asymptotically unstable and satisfy the H∞performanceindex. There is less conservatism, because this approach does not ignore any useful termswhen estimating the upper bound of the derivative of Lyapunov functional. The simulationresults illustrate the correctness and effectiveness of the proposed approach.Last, for uncertain time-varying linear delay systems with interval which is known andthe lower limit is not zero, the problem of non-fragile robust H∞controller design isstudied,based on Lyapunov stability theory and linear matrix inequality. By constructing anappropriate type of Lyapunov-Krasovskii function, combining with a new method of integralinequality, to get the time delay system is asymptotically stable and satisfy the H∞performance index of delay-dependent sufficient conditions. Then a class of non-fragilerobust H∞state feedback controller of low conservative controllers based on an ICCLalgorithm can be designed. Finally, a numerical example is given to illustrate the effectivenessof the design approach.