Output Feedback Stabilization of Switched Linear Systems with Limited Information

TL;DR

This paper introduces a control strategy for stabilizing switched linear systems with limited information, using quantized output and mode data, ensuring stability under slow-switching conditions through Lyapunov functions.

Contribution

It develops a novel encoding and control method for switched systems with limited information, guaranteeing stability despite mode switching and quantization.

Findings

Global asymptotic stability achieved under slow-switching assumptions

Constructed multiple Lyapunov functions for stability analysis

Bounded estimation error sets are effectively recalculated during switching

Abstract

We propose an encoding and control strategy for the stabilization of switched systems with limited information, supposing the controller is given for each mode. Only the quantized output and the active mode of the plant at each sampling time are transmitted to the controller. Due to switching, the active mode of the plant may be different from that of the controller in the closed-loop system. Hence if switching occurs, the quantizer must recalculate a bounded set containing the estimation error for quantization at the next sampling time. We establish the global asymptotic stability under a slow-switching assumption on dwell time and average dwell time. To this end, we construct multiple discrete-time Lyapunov functions with respect to the estimated state and the size of the bounded set.