Quantized output-feedback control of piecewise-affine systems with reachable regions of quantized measurements

Abstract

This article explores the asymptotic stability and output-feedback control issues of discrete-time piecewise-affine (PWA) systems under multi-input–multi-output (MIMO) quantization. Our work features more general and practical than those previous works focusing on single-input–single-output quantization for output-feedback control of PWA systems. We choose a PWA output-feedback controller adapting to the located region of the quantized measurement. Since the measurement outputs generally contain partial state information, the determination of the located region of the quantized measurement depends on the region where the system state dwells. Thus, the controller can operate within a reduced number of regions compared to the PWA system. The leveraged Lyapunov function incorporates the region information for both the state and the quantized measurement, as well as the MIMO quantization uncertainties. We propose a method for determining the reachable regions of the quantized measurement, based on which we conduct the stability analysis and output-feedback controller implementation subsequently. In consequence, both the conservativeness and the computational burden can be alleviated compared with the previous results that incorporated all the operating regions for output-feedback controller design. Finally, our proposed control methodology is tested via a water-tank control problem to validate its competence and strengths.