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arXiv · 2605.28665

On the Solvability of Quasi-Regulator Equations in Non-smooth Output Regulation

Zirui Niu·Daniele Astolfi·Giordano Scarciotti
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Abstract

Motivated by the prevalence of non-smooth, possibly non-periodic signals in real-world applications, the output regulation of linear systems subject to non-smooth non-periodic exogenous signals has emerged as a challenging problem. A fundamental prerequisite for solving this problem is the existence of solutions to the so-called ``quasi-regulator equations''. In this paper, we investigate the solvability of these equations. To this end, we reformulate the quasi-regulator equations as differential-algebraic equations and highlight the critical role played by the system's relative degree. We finally propose a ``non-smooth non-resonance condition'' that, under specific relative degree requirements, provides a necessary and sufficient characterization of the solvability of the quasi-regulator equations.

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Zirui Niu, Daniele Astolfi, Giordano Scarciotti. 2026-05-27. On the Solvability of Quasi-Regulator Equations in Non-smooth Output Regulation. https://arxiv.org/abs/2605.28665

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