Stability Analysis Of Complex Systems Based On Vector Lyapunov Function Method

There are lots of complex interconnected systems in real life, such as transport system, management system, control system, ecosystem and so on, which have the characteristics of large-scale, complex structures, multi-functions. The control problems of these complex interconnected systems can be transformed into the stability problems of the systems. In other words, the stability analysis is the basis and goal of the control design for complex interconnected system, and is very important for realizing the function of the system. Therefore it is necessary to study the stability of complex interconnected system.In this dissertation, aiming at neural networks and automatic vehicle following system the following subjects are studied:(1) The stability analysis method based on generalized vector Lyapunov function for a class of complex interconnected system with impulsive and time-varying delays is estabilished.(2) The stability of a class of Cohen-Grossberg neural networks with impulsive and mixed delays is studied. On the assumption that activation function satisfies Lipschitz condition and amplification function is only with lower boundary, some sufficient conditions for the stability of the system are obtained by using vector Lyapunov function and mathematics induction. Besides, based on the conception of drive-response, the global exponential synchronization problem of a class of impulsive chaotic neural networks with time-varying delays is studied. Assuming that activation functions increase monotonously, by using the theory of vector Lyapunov function and mathematics induction, some sufficient conditions for the global exponential synchronization of drive system and response system are obtained.(2) A few of neural networks with reaction-diffusion terms and impulsive and stochastic disturbance are studied. Firstly, a lemma is established to deal with the diffusion terms. Then, by using vector Lyapunov function and M matrix theory, some criteria are obtained for judging the stability of the systems. The obtained results include the influence of reaction-diffusion term on the stability of the system, and improve the conservativeness of the existing results.(3) A class of mixed delayed neural networks with Markovian jumping parameters and reaction-diffusion terms is studied. By using vector Lyapunov function and M matrix theory, some sufficient conditions for the stochastic stability of the system are obtained. Compared to the stability based on LMI approach, the obtained results are not only with simple forms, but also can be verified directly without using Matlab.(4) The stability with mode constraint for a class of nonlinear complex system with impulsive is studied. Based on the exponential stability of isolated subsystems, by using vector Lyapunov function and mathematics induction, some sufficient conditions for judging the stability with mode constraint of the system are obtained, and the exponential convergence rate is given. Then on this basis, stochastic disturbance is introduced into the model, by using stochastic box theory and Ito equation, some sufficient conditions for judging the exponential stability with mode constraint in the mean square are obtained.(5) The stability and control for a class of look-ahead vehicle longitudinal following system with impulsive effects and time-varying delays are studied. Firstly, some sufficient conditions for exponential stability of the system are obtained by applying vector Lyapunov function method and mathematical induction method. Secondly, the controller for the vehicle following system is proposed by sliding mode control method, and the stability of the controlled system is analyzed based on the obtained results. Finally, assuming that the mass of vehicles, the drag coefficient and the resistance of the ground are uncertain and bounded parameters, the controller for a class of time-varying delayed look-ahead vehicle longitudinal following system with impulsive disturbance is designed based on the idea of quasi-sliding mode control, and the stability of the controlled system is analyzed by using vector Lyapunov function.) The stability for a class of look-ahead vehicle longitudinal following system with impulsive and stochastic disturbance is studied. Firstly, by using stochastic box theory and Ito equation, some sufficient conditions for judging the exponential stability with the mode constraint in the mean square are obtained. Secondly. on this basis, the impulsive disturbance is introduced into the model. By using mathematical induction, some sufficient conditions for judging the stability with the mode constraint are obtained. Finally, the controller for the look-ahead vehicle longitudinal following system with impulsive and stochastic disturbance is designed based on the idea of sliding mode control, and the stability of the controlled system is analyzed by using vector Lyapunov function.Aiming at the stability conditions and the designed controllers for the complex systems studied in this dissertation, some numerical examples are given to verify the obtained results. It can be concluded that the obtained theorv results are correct and feasible.