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arXiv · 1809.08742

Unified Necessary and Sufficient Conditions for the Robust Stability of Interconnected Sector-Bounded Systems

Saman Cyrus·Laurent Lessard
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Abstract

Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition, but expressed in terms of relations defined on a general semi-inner product space. This increased generality leads to a clean result that can be specialized in a variety of ways. First, we show how to recover both sufficient and necessary-and-sufficient versions of the aforementioned classical results. Second, we show that suitably choosing the semi-inner product space leads to a new necessary and sufficient condition for weighted stability, which is in turn sufficient for exponential stability.

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Saman Cyrus, Laurent Lessard. 2018-09-24. Unified Necessary and Sufficient Conditions for the Robust Stability of Interconnected Sector-Bounded Systems. https://arxiv.org/abs/1809.08742

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