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arXiv · 2105.02376

A Small-Gain Theorem for Discrete-Time Convergent Systems and Its Applications

Jiayen Chen·Hendra I. Nurdin
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Abstract

Convergent, contractive or incremental stability properties of nonlinear systems have attracted interest for control tasks such as observer design, output regulation and synchronization. The convergence property plays a central role in the neuromorphic (brain-inspired) computing of reservoir computing, which seeks to harness the information processing capability of nonlinear systems. This paper presents a small-gain theorem for discrete-time output-feedback interconnected systems to be uniformly input-to-output convergent (UIOC) with outputs converging to a bounded reference output uniquely determined by the input. A small-gain theorem for interconnected time-varying discrete-time uniform input-to-output stable systems that could be of separate interest is also presented as an intermediate result. Applications of the UIOC small-gain theorem are illustrated in the design of observer-based controllers and interconnected nonlinear classical and quantum dynamical systems (as reservoir computers) for black-box system identification.

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Jiayen Chen, Hendra I. Nurdin. 2021-05-06. A Small-Gain Theorem for Discrete-Time Convergent Systems and Its Applications. https://arxiv.org/abs/2105.02376

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