Stability Analysis For Several Classes Of Lurie Systems With Time Delay

Lurie control system is a class of very typical nonlinear system. The research ofabsolute stability for Lurie control system is very important for the analysis and design ofnonlinear control system. In the real Lurie control system, time-delay phenomena usuallycause that the response property of the systems become worse, or even cause vibration andunstable phenomena. A lot of uncertain factor in process of establishing models, andvarious errors and so on, all above phenomena may occur in the real Lurie control systems,at the same time, it would influence the performance index of Lurie control systems.Therefore, it also has an important theoretical and practical significance to study theuncertain Lurie control systems with time-delay.In this paper, the problem of absolute stability and robust stability for Lurie controlsystems with time delays have been studied. Base on Lyapunov-Krasovskii stability theory,matrix theory; integral inequality and linear matrix inequality are employed in this paper.The stability for Lurie system with multiple time-varying delay, the stability for neutralLurie system with time-varying delay and the stability for neutral Lurie system withunequal discrete delay and neutral delay are studied. The main contents are as follows:Firstly, the absolute stability and robust stability of Lurie systems with multipletime-varying delay are discussed. With the delay divided into multiple segments, aLyapunov functional is introduced, combining integral-equality and linear matrixinequality technique, some delay-dependent stability criteria for Lurie control system withnonlinearities are derived, respectively. Some examples are given to illustrate theeffectiveness of the results.Secondly, the delay-dependent criteria for the absolute stability of the neutral Luriesystem with time-varying delay is obtained via Lyapunov function, integral inequality andlinear matrix inequality methods. Finally, numerical example demonstrates the validityand feasibility of the proposed.Finally, the problems of absolute stability and robust stability for neutral Luriesystem with unequal discrete delay and neutral delay are investigated. By constructing a suitable Lyapunov function, combining free-weighting matrix approach and using linearmatrix inequality technique, some sufficient conditions for the delay-dependent absolutestability and robust stability are derived. Numerical example shows the validity andfeasibility of the proposed criteria.