Fading memory and necessity of the small gain theorem

J.S. Shamma; R. Zhao; IEEE

doi:10.1109/CDC.1991.261421

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Conference proceeding

Fading memory and necessity of the small gain theorem

J.S. Shamma, R. Zhao and IEEE

[1991] Proceedings of the 30th IEEE Conference on Decision and Control, pp.788-793 vol.1

1991

DOI: https://doi.org/10.1109/CDC.1991.261421

Abstract

Control systems

Ear

Fading

Feedback

Linear systems

Nonlinear systems

Robust stability

Robustness

Time varying systems

Uncertainty

The authors consider fading memory for nonlinear time-varying systems and associated problems of robust stability. They establish notation, state some preliminary results, and consider the fading memory property. Uniform and pointwise fading memory are defined. The focus is on the differences between pointwise and uniform fading memory, and conditions are provided for an operator to have pointwise fading memory. Previous results showing that the small-gain theorem is necessary for robust stability of fading memory nonlinear systems are generalized. These results are applied to a robust stabilization problem. Conditions are presented under which a closed-loop system exhibits fading memory.< >

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Details

Title: Fading memory and necessity of the small gain theorem
Creators - without role: J.S. Shamma - Minnesota Univ., Minneapolis, MN, USA
R. Zhao - Minnesota Univ., Minneapolis, MN, USA
IEEE
Publication Details: [1991] Proceedings of the 30th IEEE Conference on Decision and Control, pp.788-793 vol.1
Publisher: IEEE
Identifiers: 9942569308331
Academic Unit: King Abdullah University of Science & Technology
Language: English
Resource Type: Conference proceeding