Quantized feedback control of linear system with performance barrier

Abstract

In this article, we investigate the quantized control problem of the continuous-time linear system with performance barrier. The performance of the system is specified by a continuous decaying function. Considering the state quantization in the feedback, a dynamic quantization scheme and a control law with limited bandwidth are developed, such that the closed-loop system is asymptotically stable and the specified performance barrier is satisfied. Based on the theory of control barrier function (CBF), the analysis on the performance guarantee of the closed-loop system under quantization is established. Furthermore, the minimal bandwidth for the quantized system with the performance barrier is explicitly given. Finally, the effectiveness of the obtained result is illustrated by an example.