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

This paper investigates the problem of H-infinity 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-infinity 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. (C) 2008 Elsevier B.V. All rights reserved.