Research On Problems Of Robust Time-delay Systems

Stochastic time-delay systems which are used to characterize the Stochastic time-delaysystems under the interference exist in reality. In the actual engineering, all kinds of randomfactors and the structure characteristics of the system cause some uncertainty, thus theresearch of robustness about the system becomes inevitable. This is the inevitable developingtrend of modern control theory and applied the way.The purpose of this article is using Lyapunov method, linear matrix inequality methodand Ito formulation to study the stability and guaranteed cost control of Stochastictime-delay systems and so on a series of problems. The main content of this paper is describedas follows:1. For a class of stochastic time-delay systems with uncertainty, robust guaranteed costcontrol problem is presented. First of all, the definitions of the robust stochastic mean squarestability and the robust guaranteed cost controller are given. Then using the Lyapunov-Krasovskii functional methods, state feedback guaranteed cost controller is obtained, whichguarantees the closed-loop system is robust stochastic mean square stability. Finally, therobust guaranteed cost control of the upper bound of performance indicators is obtained.2. TheH control problem of a class of uncertain time-delay systems is discussed.Using the Lyapunov function method, state feedback controller which ensures that theclosed-loop system is asymptotically stable is designed. And its degree ofH interferencesuppression is given.3. A class of generalized systems with time-varying delay asymptotic stability problem is considered. Applying delay decomposition method and LMIs tools, the delay-dependent asymptotic stability sufficient conditions for generalized systems is demonstrated. Software Matlab toolbox is used to calculate, and the upper bound of the maximum permissible delay of the generalized time-delay system which is ensured asymptoticallystable is determined.