Research On Stability And Sliding Mode Control Of Systems With Distributed Delays

This article studies the stability and robust adaptive sliding mode control fora class of time-delays systems and neutral type systems with distributed delays,based on the stability of time-delays systems and sliding mode control. Finally,numerical examples prove that the conclusions are efective.1.The stability of system with time-varying delay and distributed delays isinvestigated. The stability criterion is proposed in the form of LMI based onLyapunov and free weight matrices methods. Finally, the result of simulationexample show the efectiveness of the conclusion.2.The stability of neutral systems and uncertain neutral systems with time-varying delays and distributed delays are investigated. The stability criteria areproposed based on Lyapunov theory and free weight matrices methods. Finally,the numerical examples are given to illustrate the efectiveness of the method.3.The problem of robust adaptive sliding mode control for a class of sys-tems with distributed delays is investigated. By constructing the appropriateLyapunov functional, using the Lyapunov stability theory and the linear ma-trix inequality approach, a sufcient condition of globally asymptotic stabilityis given. An adaptive sliding mode controller (SMC) is proposed,the controllerovercomes efectively uncertainty infuence and makes the system get to slidingplane. Finally, the numerical example is given to illustrate the validity of themethod.4.The problem of robust adaptive sliding mode control for a class of uncertainneutral systems with distributed delays is investigated. First, by constructing asliding plane function. and then, an adaptive sliding mode controller is proposedbased on Lyapunov functional, the proposed controller can drive the system’sstate into sliding plane to obtain the desired dynamic performance. Finally, anumerical example is given to illustrate the efectiveness of the proposed slidingmode controller.