Stability Of Several Classes Of Time-Delay Systems And Their Applications

Time delay is common in many physical phenomena and engineering issues,and it often affects the dynamic behavior of the system,resulting in degradation or even instability of system performance.Therefore,the study of time-delay system has been the focus of many scholars and is of great significance.By shedding light on the estimated inequality,a focus in the research of time-delay systems' stability,this dissertation explores its relationship with the augmented Lyapunov-Krasovskii functional,and makes proposals on how to select the estimated inequality and construct the Lyapunov-Krasovskii functional.The research contents of this dissertation are as follows:First,the relationship between the augmented Lyapunov-Krasovskii functional and the estimated inequality is studied.By adopting Kronecker product representation approach,the equivalence of three inequalities of order 1 in the three categories of estimated inequalities introduced is proved,and the longitudinal relation between them is established.On the basis of it,this dissertation further studies the relationship between the estimated inequality and the augmented Lyapunov-Krasovskii functional,and analyzes the reasons why they affect the conservatism of stability conditions of time-delay systems.Second,the stability of discrete time-varying time-delay systems is studied.A discrete form of the Free-matrix-based integral inequality is obtained by adopting Schmidt orthogonalization approach.Then,by means of delay-interval division and delay-division approach,the stability criteria for discrete time-varying time-delay systems are established,and the findings obtained in this dissertation are verified to be less conservative through some numerical checks.Finally,the application of time-delay system approach in networked control system is discussed.A stability criterion with less conservatism is proposed by dividing the whole time delay system into two parts,constructing a matching Lyapunov-Krasovskii functional and adopting the Free-matrix-based integral inequality together with convex combination method.Then,the corresponding controller design approach is proposed.In the end,two numerical examples are provided to validate the effectiveness of the approach presented in this dissertation.