Study On Stability And Controllability Of Delayed Neural Networks Systems

For nonlinear systems, there are two key properties ? the stability and controllability. The stability of systems is essential for working, and the Controllability of systems is foundation for designing Control law, which show internal structure of system. Neural Networks (NNs) is a kind of nonliear dynamic systems, have complex dynamic behaviors. For success of the application in signal processing, pattern recognition, image processing and global optimization, and so on, NNs are widely studied in dynamic behaviors recently. NNs are adaptive and self-organizing systems, and a lot of their engineering applications are dependent on their stability. On the other hand, due to the influence of delay and impulse, the NNs are frequently important sources of oscillation or even chaos. Consequently, the study of stability of NNs with time delays are theoretical and practical significance. In addition, there is great progress on controllability of nonlinear systems. First, by utilizing Lyapunov stability, matrix inequality and linear matrix inequality (LMI), we research some NNs with time delays. Secondly, we study the finite-time stability of the fractional order NNs and controllability of fractional order time-delay systems. The main achievements and originality contained in this dissertation are as follows:?Asymptotical stability analysis for recurrent neural networks with time- varying delaysFor recurrent neural networks with time-varying delay, the problem of determining the global asymptotic stability is studied. By transforming the delayed neural model to describer model and then employing Lyapunov-Krasovskii stability theorem, linear matrix inequality(LMI) technique, some results are obtained. Due to the extended transformation and introducing matrix variables, the conclusions is less constraint than one which is obtained by the general model transformation.?On impulsive switching neural networksEmploying Lyapunov-Krasovskii functional and matrix inequality to impulsive switching neural networks, The robust stability of a class of impulsive switched systems with time delays and parameter uncertainties is studied. Then, the solution of matrix inequality is transformed the corresponding optimization problems. By constructing differential inequality and stability theory, exponential stability criterion of impulsive switching NNs that is obtained is few restrictions because not introduced additional variables.?Finite-time stability analysis of fractional order time-delay systemsBy fixed point theorem and operator theorem, the existence and uniqueness of mild solution for fractional impulsive neutral functional systems with nonlocal initial conditions and infinite delay is solved. Satisfying the obtained conclusion, the solutions of fractional order NNs exist. Meanwhile, a method of solving fractional order linear system is given. Finite-time stability of fractional order time-delay NNs is researched by the Generalized Gronwall Inequality and matrix inequality, and the stable time can been estimated by the obtained conclusion.?Controllability of a class of fractional order nonlinear systemsBy employing fixed point theorem and a semigroup theorem, we slove the controllability of fractional order nonlinear systems. The cotroll input is constructed in the proof process of the conclusion.