Research On Switched Neural Networks With Discrete Time-delay

A switched system is a class of hybrid system composed of several dynamical Subsystems and a switching law that specifies the active subsystem at each instant of time. Switched systems arise in many engineering applications, so It is of great practical value and theoretical significance to investigate switched systems. Switched systems with time--delay is a type of system with switching and time--delay, so its behavior character is very complex. Stable is the basic requirement for any application systems, unstable is not tolerant in any work.In this dissertation, by the basic definition and character of switched systems, some ideas and theories about control will be used to discuss the robust stability of switched neural networks and stabilization of switched dynamic neural networks and the application of these theories with some math tools, for example, Lyapunov-Krasovskii and LMI methods will be employed to analyze the robust stability of a class of switched neural networks with time-delay and the stabilization of a class of switched dynamic neural networks. And the work is arranged by the following:Firstly, preliminary data will be introduced, such as norm, vector norm, matrix norm and their characters, and there will be given some conceptions about the Lyapunov stable as well as Lyapunov stable of switched systems, otherwise, some corollaries and conclusions which will be used in the later parts are given too.Secondly, the problem about the robust stability of a class of switched neural networks with time-delay will be discussed, in this dissertation, the mathematical model about the RNNs will be proposed, and by the approach of Lyapunov-Krasovskii, the global exponential stability of this system with an arbitrary switching rule is analyzed, by the stable standard of strict linear matrix inequalities, the obtains can be used in the system with many sub-systems or with only one sut-system. In order to illustrate the effectiveness of the methodology proposed in this letter, one example about the results is proved to be valid by the digital simulation at last. Finally, the problem about the stabilization of a kind of switched neural networks with time-delay will be discussed, an approach to stabilize the switched dynamic neural networks, will be proposed by combining the theory of switched systems and dynamic neural networks, and the design is based on the technique of nonlinear inverse optimality with request to a meaningful cost function. The new result would be helpful for the control of nonlinear systems by dynamic neural networks. In order to illustrate the effectiveness of the methodology proposed in this letter, one instance about the results is proved to be valid by the digital simulation at last.