H∞ Control for Discrete-Time System With State Quantization

This paper investigates the $H_{\infty}$ control problem for a class of discrete-time systems with state quantization. Firstly, a state feedback controller is taken into the discrete-time systems in this paper. Then, the quantizer considered here is dynamic quantizer, which can be considered to be composed of a dynamic scaling and a static quantizer. The closed loop control system is asymptotically stable and satisfies the $H\infty$ performance index. Furthermore, the closed loop control system can achieve the same the $H\infty$ performance under the dynamic quantizer is taken into consideration. In addition, this paper uses the strategy to design the dynamic parameter of the quantizer which is dependent on some auxiliary scalars. The effectiveness of the controller with the state quantization design method is demonstrated by a simulation example.