Stability analysis of sampled-data switched systems with quantization

TL;DR

This paper introduces a stability analysis method for sampled-data switched linear systems with quantization, addressing mode mismatch issues and providing conditions for system stability using Lyapunov functions.

Contribution

It develops a stability analysis framework for quantized sampled-data switched systems considering mode mismatch, using a randomized algorithm to compute Lyapunov functions.

Findings

Derived a switching condition based on total mismatch time.

Established an ultimate bound on state trajectories.

Reduced the switching condition to a dwell-time criterion.

Abstract

We propose a stability analysis method for sampled-data switched linear systems with finite-level static quantizers. In the closed-loop system, information on the active mode of the plant is transmitted to the controller only at each sampling time. This limitation of switching information leads to a mode mismatch between the plant and the controller, and the system may become unstable. A mode mismatch also makes it difficult to find an attractor set to which the state trajectory converges. A switching condition for stability is characterized by the total time when the modes of the plant and the controller are different. Under the condition, we derive an ultimate bound on the state trajectories by using a common Lyapunov function computed from a randomized algorithm. The switching condition can be reduced to a dwell-time condition.