Stability Analysis For Switched Neural Networks

Artificial neural networks have become one of the main intelligent control techniques and the hot spots of international academic research. They are a kind large-scale nonlinear dynamic systems, are inspired by the human brain function and then have developed. With the development of intelligent control, switched systems have been applied widely. By using the idea of switching aid the neural networks switched neural networks are proposed. Due to switched neural networks’ great practical value and theoretical significance, switched neural networks have received great attention of researchers in recent years. But at present, the research results for the stability of switched neural networks are still insignificance. As is well known, stability of systems is premise for working, so the question is the urgent agenda. In this thesis, on the basis of the theories of switched systems, by utilizing Lyapunov function and linear matrix inequalities technology (LMIs), the stability problem of switched neural networks is suggested. The paper is arranged by the following:Firstly, the problem of the asymptotic stability of a kind of switched neural networks will be discussed. In this chapter, the mathematical model for the switched neural networks will be proposed, and by the approach of the common Lyapunov function, the single Lyapunov function and multiple Lyapunov functions combined with LMIs technology, the global asymptotic stability of this system under an arbitrary switching rule is analyzed, the sufficient conditions are given in terms of LMIs.Secondly, the problem of the asymptotic stability of a class of switched neural networks with time delay will be researched. In this section, the mathematical model about the switched neural networks with time delay(constant time delay and time-varying delay) will be provided. By employing the common Lyapunov function method, sufficient conditions are given in terms of LMIs to guarantee the asymptotic stability under arbitrary switching rule.Finally, using the average dwell time method, the asymptotic stability of a category of switched neural networks with time-varying delay will be studied. In this chapter, by constructing multiple Lyapunov functions, by utilizing the free weighting matrix and LMI technology and using the average dwell time method, the global asymptotic stability of this system under an arbitrary switching rule with the average dwell time can been obtained and the average dwell time lower bound will be presented.