Analysis And Design Of Delayed Systems Based On A Complete Delay-decomposing Approach

Time-delay is frequently encountered in systems as diverse as engineering, economics, and biology, is often a source of poor performance and instability. Based on Lyapunov-Krasovskii theory, an improved complete delay-decomposing approach is proposed by analyzing the limitations of the delay-decomposition approach. Then, by constructing new complete delay-decomposing Lyapunov-Krasovskii functions (LKF) and employing the improved free-weighting matrices method, the analysis and design of delayed systems is investigated. The main contents of the dissertation are outlined as follows,(1) The stability of linear systems with time-varying delay is discussed. For two cases of decomposing delay unequally and equally, two different Lyapunov-Krasovskii functions are constructed repectively. Without ignoring any useful information in evaluating the derivative of Lyapunov-Krasovskii functions, some new delay-dependent stability criteria are derived by introducing some free-weighting matrices to consider the relationship between the time-varying delay and its time-varying interval. The derived results are extended to linear systems with interval time-varying delay. Numerical examples are given to show the superiority of the proposed mothed over the existing ones.(2) The stability of neural networks with time-delay is investigated. Based on the complete delay-decomposing approach, a novel Lyapunov-Krasovskii function is proposed. By retaining some terms ignored in existing literatures and considering independently the upper bounds of the delay derivative in different delay interval, some generalized suficient conditions are obtained to ensure global asymptotic stability of delayed neural networks. Numerical examples are given to illustrate that the results obtained are less conservative than existing ones.(3) The passivity of neural networks with time-varying delay is addressed. Based on the complete delay-decomposing approach, different Lyapunov-Krasovskii functions are choosen in different delay interval. Without ignoring any useful information, some less conservative passivity conditions, formulated in linear matrix inequalities (LMI), are derived by introducing free-weighting matrices to consider the relationship between the time-varying delay and its time-varying interval in evaluating the derivative of Lyapunov-Krasovskii function. Numerical examples are given to show the effectiveness of the proposed mothed.(4) The stability of systems with time-delay and nolineary is investigated. Based on the quadratic separation framework and the complete delay-decomposing approach, a novel Lyapunov-Krasovskii function is constructed. Without ignoring any useful information in evaluating the derivative of Lyapunov-Krasovskii function, some new stability criteria for delayed systems with nolinearity are proposed, in which the relationship between the time-varying delay and its time-varying interval is considered by applying the improved free-weighting matrices method. Numerical examples are given to demonstrate that the results obtained are less conservative than existing ones.(5) The absolute stability of Lurie systems is investigated. Firstly, the absolute stability of Lurie system with time-varying delay is discussed. Based on a complete delay-decomposing Lyapunov-Krasovskii function and an augmented Lyapunov-Krasovskii function, respectively, two types of imporved delay-dependent absolute stability criteria are derived. Numerical examples demonstrate that the resulting criteria based on the complete delay-decomposing Lyapunov-Krasovskii function are more effective in reducing conservativeness than those based on augmented Lyapunov-Krasovskii function. Forthemore, these results are applied to the absolute stability and stabilization of Lurie network control system (NCS). Also, three LMI-based methods, based on inequality approach, parameter tuning, iterative algorithm, respectively, are given to design state feedback controller.Finally, how the complete delay-decomposing approach can be used to solve the delay-dependent stability, passitivety, and stabilization for delayed systems, is outlined. In addition, the problems with delay-dependent conditions and the direction of future studies are mentioned.