Stabilization of discrete-time piecewise affine systems with quantized signals

TL;DR

This paper presents a new quantized control method for stabilizing discrete-time piecewise affine systems, incorporating adaptive quantization and disturbance considerations to improve stability and reduce conservativeness.

Contribution

It introduces an encoding strategy for local stability and a less conservative design approach for quantized feedback controllers considering disturbances.

Findings

The proposed method achieves stabilization with quantized signals.

Adaptive quantization improves control performance near region boundaries.

The approach effectively handles bounded disturbances in system stabilization.

Abstract

This paper studies quantized control for discrete-time piecewise affine systems. For given stabilizing feedback controllers, we propose an encoding strategy for local stability. If the quantized state is near the boundaries of quantization regions, then the controller can recompute a better quantization value. For the design of quantized feedback controllers, we also consider the stabilization of piecewise affine systems with bounded disturbances. In order to derive a less conservative design method with low computational cost, we investigate a region to which the state belong in the next step.