Quantization-Uncertainty-Dependent Analysis and Control of Linear Systems With Multi-Input–Multi-Output Quantization

Abstract

This paper proposes a novel quantized control strategy for network-based linear systems subject to multi-input-multi-output (MIMO) quantization. A logarithmic quantization scheme is adopted for characterizing the quantization effect on system dynamics. A sufficient and necessary condition on the asymptotic stability is established for quantized MIMO systems. To improve the numerical testability of the obtained results, a polytopic approach approximating the MIMO quantization uncertainties is developed. By constructing a novel Lyapunov function that has dependence on the MIMO quantization uncertainties, asymptotic stability criteria are established for closed-loop quantized MIMO systems. The conditions on the existence of state-feedback controllers that guarantee the closed-loop stability are derived based on the proposed technique that decouples the controller gains and the parameters of MIMO quantization uncertainties. The proposed method and the associated theoretical results are extended to the disturbance attenuation case. Finally, the theoretical results are applied to a benchmark example and a converter circuit to illustrate their efficacy and superiority.