Quantized H ∞ Control for Time-Delay Systems with Missing Measurements

Abstract

In Chap. 2, the quantized H ∞ control problem is investigated for a class of nonlinear stochastic time-delay network-based systems with data missing, where two logarithmic quantizers are employed to quantize both the measured output and the input signals in the networked control systems. The data missing phenomena are modeled by introducing a diagonal matrix consisting of Bernoulli-distributed stochastic variables taking values 1 and 0, which means that the data from different sensors may be missing with different probabilities. Subsequently, by applying the method of sector-bound uncertainties, we obtain a sufficient condition under which the closed-loop system is stochastically stable and the controlled output satisfies the H ∞ performance constraint for all nonzero exogenous disturbances under zero initial condition. Then, we specialize the sufficient condition to some special cases with the hope that the simplified inequalities can be numerically checked more easily.