Stability Analysis And Control Design Of Two Kinds Of Time-Varying Delay Systems

Time-delay is a common phenomenon in many actual systems and is also a critical factor that directly affects and determines the stability and performance of the system.The time-delay is either constant,time-varying or random.At present,the stability analysis of linear systems with constant delay has been relatively mature,but there are still many problems in the research on time-varying delay system.For example,it is not trivial to establish delay-dependent necessary and sufficient stability conditions for time-varying delay systems.Therefore,it is particularly necessary and important to seek stability conditions with conservatism as less as possible.This thesis focuses on the stability analysis and controller design for two kinds of time-varying delay systems.One is linear systems with state time-varying delay,where the time-varying delay is continuously differentiable and the interval of delay derivative is available.The other is linear systems with sawtooth-like interval input delay,which is often employed to model networked control systems(NCSs)with event-triggering transmission scheme and interval communication delays.The main difficulty in studying the stability analysis for the two kinds of systems is how to fully utilize the available information on time-varying delay to construct a dedicated Lyapunov-Krasovskii functional(LKF)and relevant enlargement inequality techniques.For this reason,the specific research contents are as follows:(1)For the linear continuous system with time-varying delay,its delay-and-delayderivative-dependent stability conditions and control design conditions are derived.A new delay-dependent augmented LKF is proposed by using Legendre polynomials of order and information on time-vary delay,and the positive definiteness constraint of the matrix variables in the LKF is relaxed.Then,a -order Bessel-Legendre(B-L)inequality,a reciprocally convex combination and a novel quadratic convex lemma are used to estimating the upper bound of the derivative of the LKF.The delay-and-delay-derivative-dependent stability conditions and controller design conditions are provided in the form of tractable linear matrix inequalities(LMIs).In the numerical example,by comparing with the stability conditions proposed by some existing literature,the less conservatism of the obtained conditions and the effectiveness of the control design are verified.(2)The NCS with the sampling behavior,event-triggering transmission scheme and interval communication delays is modeled as a system with sawtooth-like input delay,and the stability analysis and networked controller design of the system are studied by utilizing the relationship among the input delay,sampling period and interval communication delays.Considering the periodic data sampling and the limited network bandwidth,an eventtriggering transmission scheme is introduced to save network and computing resources.Under this scheme,the relationship among the upper bounds of the input delay and communication delays and the sampling period is further exploited.The B-L inequality method is reevaluated for the stability analysis of the NCS,and a new discontinuous augmented LKF is tailored for the second-order B-L inequality.A matrix-based quadratic convex combination enlargement inequality is proposed by using the relationship between the double delays in analysis results.The delay-dependent stability conditions and network-based controller design results are derived in terms of LMIs.A numerical example is given to illustrate the influence of introducing the upper bound information of communication delays on the stability analysis results.The superiority of the proposed methods and the effectiveness of the control design are demonstrated by the comparison with the results obtained in some existing literature.To end this thesis,the research and contributions of this thesis are summarized.Some remaining problems,as well as meaningful research directions of time-varying delay systems,especially the NCSs modeled by input delay system methods.