This paper investigates the problem of exponential dissipativity for stochastic systems with repeated scalar nonlinearities. The nonlinear system is described by a state equation containing a repeated scalar nonlinearity, which typically appears in recurrent neural networks. Attention is focused on the exponential dissipativity analysis of stochastic systems with repeated scalar nonlinearities with respect to quadratic supply rates. Passive and non-expansive property of stochastic systems with repeated scalar nonlinearities is also characterized. Moreover, a controller has been designed to make the stochastic systems with repeated scalar nonlinearities asymptotically stable. A Marketing-Production system and a Chua circuit are given to illustrate the effectiveness of the proposed design method.
['Cihui Yang', 'Zhigang Zeng', 'Shiping Wen']
Dissipativity Analysis and Stabilization for Stochastic Systems with Repeated Scalar Nonlinearities and Applications