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Observer-based $H_\infty$ control for systems with repeated scalar nonlinearities and multiple packet losses. (English) Zbl 1206.93035
Summary: This paper is concerned with the $H_\infty$ control problem for a class of systems with repeated scalar nonlinearities and multiple missing measurements. The nonlinear system is described by a discrete-time state equation involving a repeated scalar nonlinearity, which typically appears in recurrent neural networks. The measurement missing phenomenon is assumed to occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator, where the missing probability for each sensor/actuator is governed by an individual random variable satisfying a certain probabilistic distribution in the interval $[0,1]$. Attention is focused on the analysis and design of an observer-based feedback controller such that the closed-loop control system is stochastically stable and preserves a guaranteed $H_\infty$ performance. Sufficient conditions are obtained for the existence of admissible controllers. It is shown that the controller design problem under consideration is solvable if certain Linear Matrix Inequalities (LMIs) are feasible. Three examples are provided to illustrate the effectiveness of the developed theoretical results.

##### MSC:
 93B36 $H^\infty$-control 93E15 Stochastic stability 93C55 Discrete-time control systems
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