Robust Stability Analysis And H_∞Controller Design For Time-Delay System

Time-delay phenomenon widely exists in natural world. It usuallycauses the system performance deteriorative and is also a main source tomake the system unstable. The study of time-delay system has alwaysbeen a hot issue, which attracts widespread attention.This is a special case for the time-delay system, namely neutraltime-delay system. It means that the delay term not only exists in thestate variables of the system, but also in their derivatives. It is morecomplicated and worth studying than general time-delay system.The main research work and conclusions of this paper are asfollowed.1)Focus on robust stability problem of uncertain neutral time-delaysystem. Based on Lyapunov method, by constructing a newLyapunov-Krasovskii functional, combining with linear matrixinequality(LMI), it deduces the conditions to make the uncertain neutraltime-delay system stable. By numerical examples, it shows thesuperiority of the method in this paper by comparing with the previousresults.2)Focus on theH￥control problem of uncertain neutral time-delaysystem. By constructing a Lyapunov-Krasovskii functional, adopting theparameter adjustment method and combining with linear matrixinequality(LMI), it deduces the determinant conditions of robust stabilityof uncertain neutral time-delay system and the existence conditions of itsH_∞￥controller. Then, it shows the effectiveness of the method in thispaper by numerical example simulation and Simulink.3) With studying the single machine infinite bus system, combiningwith some dynamic balance equations of the synchronous motor, somedynamic equations in exciter and PSS time-delay system. Then,linearizing them at the equilibrium point, establish a mathematicalmodel based on WAMS power time-delay system. Using Lyapunovmethod, by constructing a Lyapunov-Krasovskii functional andcombining with LMI, it deduces the asymptotic stability conditions of electrical time-delay system, and shows the superiority of the method inthis paper by numerical example simulation.