H_∞Control Of Switched Neural Network Systems

The neural networks are a kind of large-scale complex nonlinear system, which possess abundant dynamic behaviors. In recent years, the switch thought has been introduced into the neural networks. The switched neural networks, consisting of a family of neural networks, have received great attention of researchers as its wide practical applications and theoretical significance. Stability is foundation of a system, and the researches of switched neural networks are mainly for the stability of the system at present. Based on the theory of switched systems, H∞control of switched neural networks is studied in this paper. The paper is divided as follows:The problems of stability and H∞solvable for switched neural networks under arbitrarily switching sequences are researched in this paper. Sufficient conditions are obtained which guarantee the asymptotically stability and H∞solvable of the switched neural networks for any switching signal. The single Lyapunov functions method is employed to design the switching rule when each subsystem is not satisfy H∞solvable, to guarantee the switched networks is H∞solvable. The results are given in terms of linear matrix inequalities (LMI), and a numerical example is provided to prove the effectiveness and feasibility of the proposed method.H∞solvable problems are discussed respectively for the delayed switched Hopfield and CNN neural networks under arbitrarily switching sequences. Sufficient conditions are given for the perturbed switched neutral networks by using common Lyapunov functions methods and linear matrix inequality technique.The H∞control problems of the delayed switched Hopfield and CNN neural networks are considered in this paper. State feedback controllers of H∞are designed respectively not only to guarantee the asymptotical stability of the perturbed switched neutral networks, but also reduce the effect of external disturbance to a certain constraint.To conclusion, the paper indicates some problems are proposed which would be studied in the further.