The necessity of the small-gain theorem for time-varying and nonlinear systems

J.S. Shamma

doi:10.1109/9.90227

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The necessity of the small-gain theorem for time-varying and nonlinear systems

Journal article

Peer reviewed

The necessity of the small-gain theorem for time-varying and nonlinear systems

J.S. Shamma

IEEE transactions on automatic control, Vol.36(10), pp.1138-1147

01/10/1991

DOI: https://doi.org/10.1109/9.90227

Abstract

Fading

Feedback

Nonlinear systems

Robust stability

Robustness

Sufficient conditions

Time varying systems

Uncertainty

It is shown that an appropriately modified version of the small-gain theorem which uses the 'asymptotic gain' of a fading-memory system leads to a necessary and sufficient condition for the stable invertibility of certain feedback operators. This modified small-gain theorem is then used to obtain conditions for robust finite-energy input-output stability of: (1) nonlinear plants subject to nonlinear time-varying perturbations; and (2) linear time-varying plants subject to linear time-varying perturbations. These conditions are shown to be necessary as well as sufficient.< >

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Title: The necessity of the small-gain theorem for time-varying and nonlinear systems
Creators - without role: J.S. Shamma - University of Minnesota
Publication Details: IEEE transactions on automatic control, Vol.36(10), pp.1138-1147
Publisher: IEEE
Identifiers: 9944161608331
Academic Unit: King Abdullah University of Science & Technology
Language: English
Resource Type: Journal article