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arXiv · 2504.21493

Stabilization of linear systems with multiple unknown time-varying input delays by linear time-varying feedback

Bin Zhou·Kai Zhang
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Abstract

This paper addresses the stabilization of linear systems with multiple time-varying input delays. In scenarios where neither the exact delays information nor their bound is known, we propose a class of linear time-varying state feedback controllers by using the solution to a parametric Lyapunov equation (PLE). By leveraging the properties of the solution to the PLE and constructing a time-varying Lyapunov-Krasovskii-like functional, we prove that (the zero solution of) the closed-loop system is asymptotically stable. Furthermore, this result is extended to the observer-based output feedback case. The notable characteristic of these controllers is their utilization of linear time-varying gains. Furthermore, they are designed entirely independent of any knowledge of the time delays, resulting in controllers that are exceedingly easy to implement. Finally, a numerical example demonstrates the effectiveness of the proposed approaches.

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Bin Zhou, Kai Zhang. 2025-04-30. Stabilization of linear systems with multiple unknown time-varying input delays by linear time-varying feedback. https://doi.org/10.1016/j.automatica.2025.112175

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