A Small-Gain Theorem for Monotone Systems with Multi-Valued Input-State Characteristics

Details A Small-Gain Theorem for Monotone Systems with Multi-Valued Input-State Characteristics A Small-Gain Theorem for Monotone Systems with Multi-Valued Input-State Characteristics

2005-06-24

arxiv.org/abs/math/0506508v1

IEEE Transactions on Automatic Control, Volume 51, Number 2, pp. 287-292, February 2006

Mathematics

Optimization and Control

17 pages, 2 figures, to appear in IEEE Transactions on Automatic Control

Scientific paper

10.1109/TAC.2005.863534

We provide a new global small-gain theorem for feedback interconnections of monotone input-output systems with multi-valued input-state characteristics. This extends a recent small-gain theorem of Angeli and Sontag for monotone systems with singleton-valued characteristics. We prove our theorem using Thieme's convergence theory for asymptotically autonomous systems. An illustrative example is also provided.

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