State Feedback H∞ Control for Networked Control Systems with Quantization and Random Communication Delays

In this paper, the state feedback H∞ control problem for networked control systems with quantization and random communication delays is discussed. The random delays from the sensor to the controller and from the controller to the actuator are considered. The quantizer considered here is dynamic and composed of an adjustable zoom parameter and a static quantizer. A novel quantized random delay model is proposed, and by using this model, the relationship of the quantizations, delays and the system performance is studied. The state feedback H∞ controller can be constructed via solving a linear matrix inequality. With a condition on the quantization range and the error bound satisfied, a quantized H∞ control strategy is derived such that the closed-loop system with quantization and random delays exponentially mean-square stable and with a prescribed H∞ performance bound. An example is presented to illustrate the effectiveness of the proposed method.