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arXiv · 2604.26455

Fixed-Time and Arbitrarily Fast Exponential Stabilization of Discrete-Time Switched Linear Systems

Picchiotti Flavio·Thiago Alves Lima·Girard Antoine
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Abstract

In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps, independently of the switching sequence. We address both the mode-dependent case, where the controller has access to the active mode, and the mode-independent case, where a common feedback law must be employed. For each setting, we present constructive procedures to compute the stabilizing state-feedback gains. Building on these results, we then introduce a structural decomposition of switched systems, which serves to simplify stabilizability analysis and controller design. This allows us to establish the equivalence between fixed-time stabilizability and arbitrarily fast exponential stabilizability. The effectiveness of the proposed methods is illustrated through a numerical example.

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Picchiotti Flavio, Thiago Alves Lima, Girard Antoine. 2026-04-29. Fixed-Time and Arbitrarily Fast Exponential Stabilization of Discrete-Time Switched Linear Systems. https://arxiv.org/abs/2604.26455

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