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arXiv · 2101.01900

Generalized Necessary and Sufficient Robust Boundedness Results for Feedback Systems

Saman Cyrus·Laurent Lessard
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Abstract

Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for arbitrary semi-inner product spaces. Our result is purely algebraic, and holds even when the conventional discrete or continuous-time causal dynamical systems are replaced by general nonlinear relations, where there need not exist a notion of time. Our result clarifies when the sufficient conditions for robust stability are also necessary, and explains why stronger assumptions such as linearity and time-invariance are typically needed to prove necessity in the conventional dynamical systems setting.

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Saman Cyrus, Laurent Lessard. 2021-01-06. Generalized Necessary and Sufficient Robust Boundedness Results for Feedback Systems. https://arxiv.org/abs/2101.01900

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