Analysis And Synthesis For Several Classes Of Time Delayed Lur’e Or Lur’e Type Systems

Lur’e system is a kind of nonlinear system that the nonlinear term is treated in the finite sector area (finite Hurwitz sector) or in the infinite sector area (infinite Hurwitz sector). In the research work of Lur’e system or Lur’e type system, both the inertial element and network transmission will lead to time delay. On one hand, time delay is often considered to be ubiquitous in the real world and is common in various practical application fields; on the other hand, system instability is mainly due to the intrinsic time delay, more and more researchers have stated that the phenomenon of time delay existing in dynamical systems cannot be ignored in stability analysis of such systems; on the other hand, there always exists the uncertainty in real systems. In a word, the entire makes the study of time delayed absolutely stability or robust absolutely stability important in the theorical research.In this dissertation, based on LMI, convex method and Lyapunov-Krasovskii theorem, analysis and synthesis for several classes of time delayed Lur’e and Lur’e type systems are studied. The following topics are discussed such as time delayed Lur’e system, uncertain time delayed Lur’e system, Lur’e type time-delay complex network, multi-delay Lur’e network control systems (NCSs), H∞control synthesis for multi-delay Lur’e network control systems and stability analysis of time delayed neural networks. The main contents of this dissertation are described as follows:1. Chapter two deals with the absolute stability analysis for Lur’e system with interval time-delay and norm bounded parameter uncertainties. By constructing the Lyapunov-Krasovskii functional, some new delay-dependent robust stability criteria are obtained in terms of linear matrix inequalities (LMIs) with convex combination technique. The resulting criterion has advantages over some previous ones. The numerical examples illustrate that the obtained absolute stability criteria are less conservative than previous ones.2. Chapter three investigates the H∞control synthesis problem for Lur’e networked control systems with multiple time-varying delays. The stable controller design and H∞synthesis approaches are derived in the form of linear matrix inequalities. Finally, a set of numerical examples are studied and the results demonstrate the applicability and effectiveness of the suggested approaches.3. Chapter four is concerned with the synchronization problem for Lur’e type dynamical complex networks with time-varying delay. By using and eigenvalue-decoupling method, high-dimension criteria are decoupled into low-dimension ones and the complexity of the criterion computation is reduced. Then the numerical examples are carried out to demonstrate the applicability and effectiveness of the proposed work through simulations.4. Chapter five is concerned with the problem of stability for recurrent neural networks with time-delay. By choosing a new class of Lyapunov-Krasovskii functional, the conditions of constant delay and time-varying delay are both studied. Then, a numerical example is carried out to demonstrate the applicability and effectiveness of the proposed work through simulations.At the end of this dissertation, a review of the recent results on the study the several classes system with time-delay and nonlinearities has been made and the prospect of the further research interests has been given.