Robust Finite-time Stabilization of Linear Systems with Limited State Quantization - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles Automatica Year : 2025

Robust Finite-time Stabilization of Linear Systems with Limited State Quantization

Abstract

This paper investigates the robust asymptotic stabilization of a linear time-invariant (LTI) system by static feedback with a static state quantization. It is shown that the controllable LTI system can be stabilized to zero in a finite time by means of nonlinear feedback with a quantizer having a limited (finite) number of values (quantization seeds) even when all parameters of the controller and the quantizer are time-invariant. The control design is based on generalized homogeneity. A homogeneous spherical quantizer is introduced. The static homogeneous feedback is shown to be a local (or global) finite-time stabilizer for any controllable linear system (depending on the system matrix). The tuning rules for both the quantizer and the feedback law are obtained in the form of Linear Matrix Inequalities (LMIs). The closed-loop system is proven to be robust with respect to some bounded matched and vanishing mismatched perturbations. Theoretical results are supported by numerical simulations.

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Dates and versions

hal-04757031 , version 1 (28-10-2024)

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Yu Zhou, Andrey Polyakov, Gang Zheng. Robust Finite-time Stabilization of Linear Systems with Limited State Quantization. Automatica, 2025, 171, pp.111967. ⟨10.1016/j.automatica.2024.111967⟩. ⟨hal-04757031⟩
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