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arXiv · 2608.01699

On input-output persistency and the interconnection of positive nonlinear systems

Arthut Castello B. de Oliveira·Moh K. Wafi·Eduardo D. Sontag
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Abstract

In this paper we study feedback interconnections of positive nonlinear SISO systems and introduce two complementary properties: persistent-input/persistent-output (PIPO) for the plant and persistent-input/transient-output (PITO) for the controller. Assuming forward completeness of the closed loop and a one-sided affine growth bound on the controller output, we show that PIPO and PITO jointly imply boundedness of the control signal. The result is input-output in nature and does not require linearity or monotonicity of the interconnected subsystems, although it does not in general guarantee boundedness of the full controller state. We provide a structural PIPO condition for positive monotone plants with a class-\(\mathcal K_\infty\) steady-state characteristic, establish PITO for the antithetic integral controller with explicit gains, and illustrate the framework on a nonlinear integral-feedback motif with multiplicative controller growth.

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Arthut Castello B. de Oliveira, Moh K. Wafi, Eduardo D. Sontag. 2026-08-03. On input-output persistency and the interconnection of positive nonlinear systems. https://arxiv.org/abs/2608.01699

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