Stability Analysis And Controller Design For A Class Of Time-delay Systems Based On L-K Functional

As we all know,the stability,as the basic requirement of control systems,may be destroyed due to the presence of time delays.In the actual control systems,time delay is always existent,which makes the system performance worse,the study of time-delay system has important theoretical value and practical significance.Time-delay systems are a particular class of infinite dimensional systems,which have complicated dynamic properties.Hence,a great deal of scholars have studied linear time-delay systems,a large number of research results on the stability of linear time-delay systems has achieved.However,most of systems are nonlinear in engineering,the research on nonlinear time-delay systems is equally important,and the direct analysis and control of nonlinear systems are difficult.The T-S fuzzy model builds a bridge between fuzzy logic theory and linear systems theory,therefore,it provides a good opportunity to employ the well-established linear systems theory for theoretical analysis and synthesis of the T-S fuzzy system,the T-S fuzzy model provides an effective analysis method for the research of nonlinear systems.In this paper,the stability of linear time-delay system and T-S fuzzy time-delay system is analyzed.Meanwhile,considering that the stability of the system will be affected by itself and other factors,the controller design is carried out.Finally,the observer design is carried out in this case that the state of the system cannot be measured directly.This paper will study from the following aspects:(1)The improvement of stability criteria for a class of time-varying delay systems is considered.The Lyapunov Krasovskii(L-K)functional is constructed by introducing an augmented matrix and an improved triple integral term.The integral terms from the derivation of L-K functional are dealt with by proper definition technique.The stability criterion and the sufficient condition of the controller for time-varying delay systems with less conservatism and high computational efficiency is obtained in the form of LMIs.Several numerical examples and Simulink simulations are included to verify the effectiveness of the stability criterion and the controller design scheme.(2)Consider the stability analysis and controller design for a class of T-S fuzzy time-varying delay systems.In order to obtain better results,the Lyapunov Krasovskii(L-K)functional is constructed by introducing the fuzzy line integral and several triple integral terms.Stability criterion and controller design criterion for time-varying delay systems with less conservatism is obtained.Finally,the effectiveness of the controller is verified by simulation.(3)After the stability and controller design of nonlinear time-delay systems are studied,considering the situation that the state of the system cannot be measured,based on T-S fuzzy system with constant time delay,the system is reconstructed to estimate the state of the original system.Based on the observer,an output feedback controller is designed to improve the system performance.Finally,the validity of the stability criterion and controller design scheme is verified by simulation.