Stability Analysis Of Several Kinds Of Time-delay Systems

Time delay is very common in practical systems,such as digital control systems,long transmission lines in pneumatic systems,manufacturing process es,and remote control systems,which may lead to poor or even unstable system performance.Time delay is a common phenomenon in singular systems.Since the singular system model includes not only dynamic equations,but also algebraic constraints,the singular system is a more extensive form of dynamic system than the normal delay system,which can more accurately describe the actual dynamic systems.As a class of differential systems with discrete delay,neutral delay and distributed delay,neutral distributed time-delay systems can more accurately describe practical problems.It appears in numerous areas of engineering practice,such as heat exchangers,robotic exposure to rigid environments,laser optics,distributed networks,lossless transfer lines,and more.In this paper,based on linear matrix inequality(LMI)technique,the problems of admissibility of singular time-delay systems and stability of neutral systems with distributed delay are studied in detail by analyzing and improving the existing methods and conclusions.The specific research contents are summarized as follows:(1)Neutral system approach is adopted to study the admissibility of a class of singular systems with time-varying delay.Firstly,the neutral system approach is used to transform singular time-varying delay systems into neutral time-varying delay systems on the basis of ensuring that singular time-varying delay systems are regular and impulse free.Secondly,an augmented Lyapunov-Krasovskii functional(LKF)is proposed,and a quadruple integral term is added to the LKF to obtain more time delay information.Thirdly,the fourth-order Bessel-Legendre integral inequality(B-L integral inequality)and the double third-order B-L integral inequality are used to deal with the integral terms of LKF after derivation,and the stability condition of neutral time-varying delay systems is obtained,and then the admissibility condition for singular time-varying delay systems is obtained.Finally,a numerical example is employed to illustrate the feasibility and effectiveness of the proposed results.(2)For the neutral system with distributed delay,the LKF with augmented terms is selected,and a quadruple integral term is added to the LKF to obtain more delay information.Then the fourth-order B-L integral inequality and double third-order B-L integral inequality are used to deal with the integral terms of LKF after derivation,so that the conservatism of the system can be effectively reduced,and the stability condition of neutral systems with distributed time delay is obtained.Finally,the feasibility and effectiveness of the results are verified by numerical examples,which shows that the proposed method has greater advantages than the existing methods.