H∞H∞ filtering for systems with repeated scalar nonlinearities under unreliable communication links

This paper investigates the problem of H∞H∞ filtering for systems with repeated scalar nonlinearities under unreliable communication links. The nonlinear system is described by a discrete-time state equation containing a repeated scalar nonlinearity as in recurrent neural networks. The communication links, existing between the plant and filter, are assumed to be imperfect and a stochastic variable satisfying the Bernoulli random binary distribution is utilized to model the phenomenon of the measurements missing. Attention is focused on the analysis and design of stable full- and reduced-order filters with the same repeated scalar nonlinearities such that the filtering error system is stochastically stable and preserves a guaranteed H∞H∞ performance. Sufficient conditions are obtained for the existence of admissible filters. Since these conditions involve matrix equalities, the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities, which can be readily solved by using standard numerical software. A numerical example is given to illustrate the effectiveness of the proposed design method.