Input-to-state stabilization of linear systems under data-rate constraints

Jul 16, 2026

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Feedback stabilization for linear systems under data-rate constraints is addressed in the presence of completely unknown disturbances. A sampled and quantized state-measurement communication/control strategy is developed, where the quantization range is adaptively tuned using reachable-set approximations and disturbance estimates inferred from quantization parameters. The method alternates stabilizing and searching phases to recover the state after quantization-range escapes. A data-rate condition yields input-to-state stability (ISS) relative to the disturbance, with an extra quantization symbol ensuring ISS near equilibrium, validated by simulation.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages24

Reading Time1 h 0 min

Introduction

Data-rate constraints in networked control

Quantization schemes and prior ISS/practical ISS results

Contributions and organization

arXiv :2603 .28016v2 [ ee ss . SY] 11 Jul 2026 Input-to-state stabilization of linear systems under data-rate constraints Mahmoud Zamani and Guosong Yang∗ Abstract We study feedback stabilization of linear systems under data-rate constraints in the presence of completely unknown disturbances. A communication and control strategy is proposed based on sampled and quantized state measurements, where the quantization range is dynamically adjusted using reachable-set approximations and disturbance estimates derived from quantization parameters. The strategy alternates between stabilizing and searching stages to recapture the state after escapes from the quantization range. Under a data-rate condition, it guarantees input-to-state stability (ISS) with respect to the disturbance. An additional quantization symbol is introduced to establish ISS near the equilibrium. A simulation example illustrates the effectiveness of the proposed approach. 1 Introduction Feedback control under data-rate constraints has been an active research area for decades, as surveyed in, e.g.,[1–3] . Such constraints arise naturally in networked control systems due to communication costs, bandwidth limitations, and security considerations. Beyond these practical motivations, a fundamental question is how much information is required to achieve a given control objective. A widely used framework for achieving finite data rate is to generate the control input from sampled and quantized state measurements taking values in a finite set. Beginning with [4–10], various quantization schemes have been developed for stabilizing linear systems. In particular, asymptotic stabilization under finite data rate requires dynamic adjustment of the size of the quantization range (zooming) [6–10], while the required data rate can be reduced by dynamically adjusting its center as well (moving-center quantization)[8–10] . These ideas have subsequently been extended to nonlinear systems [7, 11, 12] and switched systems [13, 14] . We consider feedback stabilization under data-rate constraints in the presence of unknown disturbances. In [8, 10], a known bound on the disturbance is assumed, and the minimum data rate required for asymptotic stabilization is characterized. Without such a bound, the problem becomes significantly more challenging, as disturbances may drive the state outside the quantization range after capture. In this setting,[15] established input-to-state stability (ISS) [16] using dynamic quantization with alternating zooming-out and zooming-in stages. Similar ISS results were obtained in [17] using logarithmic quantization in polar coordinates, and in [18] using moving-center quantization with improved data-rate efficiency. However, the fixed-center quantization schemes in [15, 17] lead to implicit and generally conservative data-rate bounds, whereas the ∗The authors are with the Department of Electrical and Computer Engineering, Rutgers University–New Brunswick, Piscataway, NJ 08854 USA (e-mails: {mahmoud.zamani, [guosong.yang}@rutgers.edu](guosong.yang}@rutgers.edu)). moving-center scheme in [18] relies on additional mechanisms such as a dedicated escape-detection mode and quantizer resets. More recently, [14] proposed a disturbance-estimation framework for switched linear systems that avoids these complexities, but achieves only the weaker property of practical ISS [19] . This paper addresses these limitations for linear systems with completely unknown disturbances. Extending the disturbance-estimation idea of [14], we propose a communication and control strategy that combines the data-rate efficiency of moving-center quantization with a Lyapunov-based design and eliminates the need for a dedicated escape-detection mode or quantizer resets. Our results provide an explicit characterization of the admissible data rate and establish ISS rather than practical ISS. To this end, we design a disturbance estimate derived from quantization paramet

FAQs

What problem is studied in this paper?

The paper studies feedback stabilization of linear linear systems under data-rate constraints when disturbances are completely unknown.

How does the proposed strategy handle quantization range limitations?

It alternates stabilizing and searching stages, using reachable-set approximations and disturbance estimates to recover the state after it escapes the quantization range.

What stability guarantee is obtained under an admissible data rate?

Under a data-rate condition, the method guarantees input-to-state stability (ISS) with respect to the disturbance, including ISS near the equilibrium via an additional quantization symbol.

Jul 16, 2026

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