Research On The Absolute Stability For Lurie Control Systems With Time-delays

Lurie control systems are a class of very typical nonlinear systems with nonlinearities constrained in the finite Hurwitz sector or infinite one, the problem of absolute stability for Lurie systems have attracted much attention. Since time-delays are frequently encountered in various systems, and are often the sources of instability, the study of absolute stability for Lurie systems is of great theoretical and practical meaning. The absolute stability of Lurie control systems with time-delays and nonlinearities are considered in this thesis. Based on Lyapunov stability theory, by constructing a suitable Lyapunov-krasovskii functional and with linear matrix inequality (LMI) as research means, on the one hand, delay-dependent sufficient condition for the absolute stability is derived by introducing some free-weighting matrices and combining a new integral inequality, this method does not employ any model transformation technique, according to an improved integral inequality, transformates the integral terms, which contain the information for time. This method gets less conservative than those employing model transformations, on the other hand, delay-dependent and delay-independent sufficient conditions for the absolute stability are obtained by Schur complement lemma, the S-procedure method, the combination of essential matrix theory and corresponding inequality techniques. Some of the results are extended to uncertain Lurie control systems with time-delays. The main contents of this thesis are outlined as follows:(1) The absolute stability of Lurie control system with state time-delays is discussed. By choosing a suitable subsection Lyapunov function and combing a improved integral inequality, the delay-dependent sufficient conditions for the absolute stability of Lurie control systems with finite sector-bounded nonlinearity and infinite sector-bounded nonlinearity are derived. Simultaneously, several corresponding numerical examples are given to illustrate the effectiveness of the results.(2) The absolute stability of Lurie system with control time-delays is discussed. Both delay-independent and delay-dependent sufficient conditions for the absolute stability are obtained by choosing a suitable Lyapunov function.(3) Lurie control system with multiple time-delays is considered. Using the method mentioned above, sufficient conditions for the absolute stability of Lurie system are obtained by leading a proper zero term containing some free-weigh ting matrices.(4) Uncertain Lurie control system is considered. Delay-dependent sufficient conditions for the absolute stability of uncertain Lurie control system are obtained by extending some above results. At last, several corresponding numerical examples are given to illustrate the effectiveness of the results. These conditions above are all formulated in the form of linear matrix inequalities(LMIs), which could be solved easily by Matlab Toolbox.