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Quantized $$H_{\infty }$$ control for networked systems with communication constraints. (English) Zbl 1286.93163
Summary: The problem of quantized $$H_{\infty }$$ control for Networked Control Systems (NCSs) subject to time-varying delay and multiple packet dropouts is investigated in this paper. Both the control input and the measurement output signals are quantized before being transmitted and the quantized errors are described as sector bound uncertainties. The measurement channel and the control channel packet dropouts are considered simultaneously, and the stochastic variables satisfying Bernoulli random binary distribution are utilized to model the random multiple packet dropouts. Sufficient conditions for the existence of an observer-based controller are established to ensure the exponential mean-square stablility of the closed-loop system and achieve the optimal $$H_{\infty }$$ disturbance attenuation level. By using a globally convergent algorithm involving convex optimization, the nonconvex feasibility can be solved successfully. Finally, a numerical example is given to illustrate the effectiveness and applicability of the proposed method.

##### MSC:
 93E03 Stochastic systems in control theory (general) 93C55 Discrete-time control/observation systems 93E12 Identification in stochastic control theory 93B36 $$H^\infty$$-control
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