Finite-time Stability And Control Of Several Types Of Time-delayed Systems

Stability has always been a major concern when modelling and analysing systems.In general,Lyapunov asymptotic stability can meet the requirements of engineering,however,Lyapunov stability only reflects the steady-state performance of the system and does not reflect the transient properties of the system.This leads to the fact that Lyapunov stability theory is not applicable in some practical engineering situations where the response time is fast and short.In contrast to the traditional Lyapunov stability,this paper studies the finite-time stability of a system.Finite-time stability refers to the fact that given the initial state of a system,the system state always remains within a pre-given upper bound within a certain time frame.This is used to study systems that need to meet certain transient performance requirements,such as network communication systems,rocket launch systems,high-precision robotic arms,etc.This paper focuses on the design of finite-time stability performance and associated controllers for several types of time-delay related systems,with the main work covering the following aspects.1.Finite-time stability analysis of linear pulsed stochastic time-delay systems and the design of the corresponding controllers.A suitable Lyapunov-Krasovskii function is first constructed,and then three different types of pulses,namely sedentary,anti-sedentary and neutral,are investigated using stochastic analysis techniques,the average pulse interval condition,Schur complementary inducements and MATLAB’s linear matrix inequality(LMI)toolbox to derive sufficient conditions for the finite-time stability of the system.2.We extend the impulsive stochastic time-delay system to impulsive stochastic time-delay systems containing uncertain terms,and the application of impulsive stochastic time-delay systems to neural networks.The mean-square finite-time stability performance of the above two types of systems are obtained respectively,based on certain assumptions holding,and the correctness of the sufficient conditions is verified by the mean-square trajectory plots of the systems.3.The finite-time stability of time-delay systems is further investigated considering the important role of time delays in the system.A Lyapunov-Krasovskii function containing triple integrals is constructed,and the stability conditions associated with the time delay are obtained by deflating the integral terms after derivation using matrix inequality lemmas.In addition to this,the chapter extends the concept of finite-time stability to investigate the input-output finite-time stability of the system.