Quantized Feedback Stabilization of Sampled-Data Switched Linear Systems

TL;DR

This paper develops a stability analysis method for sampled-data switched linear systems with quantization, addressing mode mismatch and quantization effects to ensure system stability.

Contribution

It introduces a sufficient condition based on total mismatch time for stability, linking mismatch duration with switching dwell time.

Findings

Stability can be guaranteed under bounded mismatch time.

Quantization effects cause trajectory wandering around the origin.

Relationship between mismatch time and switching dwell time is established.

Abstract

We propose a stability analysis method for sampled-data switched linear systems with quantization. The available information to the controller is limited: the quantized state and switching signal at each sampling time. Switching between sampling times can produce the mismatch of the modes between the plant and the controller. Moreover, the coarseness of quantization makes the trajectory wander around, not approach, the origin. Hence the trajectory may leave the desired neighborhood if the mismatch leads to instability of the closed-loop system. For the stability of the switched systems, we develop a sufficient condition characterized by the total mismatch time. The relationship between the mismatch time and the dwell time of the switching signal is also discussed.