Journal ArticleDOI
Essays on the absolute stability theory
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A brief historical background of the development of the absolute stability theory was presented, and some of its methods and approaches, as well as the results obtained using them, were discussed as discussed by the authors.Abstract:
A brief historical background of the development of the absolute stability theory was presented, and some of its methods and approaches, as well as the results obtained using them, were discussed. The kinds of systems under consideration are named, and applications of the methods and results of the absolute stability theory to other scientific and practical fields for solution of the engineering, mechanical, physical, and other problems were presented.read more
Citations
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Journal ArticleDOI
Hidden Attractors in Dynamical Systems. From Hidden Oscillations in Hilbert-Kolmogorov Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits
TL;DR: The problem of investigating hidden oscillations arose in the second part of Hilbert's 16th problem (1900), and the first nontrivial results were obtained in Bautin's works, which revealed no similar transient processes leading to such attractors.
Journal ArticleDOI
Infinite-Dimensional Feedback Systems: The Circle Criterion and Input-to-State Stability
TL;DR: An overview of the circle criterion and its connection with ISS is provided, concerned with the analysis of a feedback interconnection of Lure type, which consists of a linear system in the forward path and a sector-bounded nonlinearity in the negative feedback path.
Journal ArticleDOI
Kalman-Popov-Yakubovich lemma and the S-procedure: A historical essay
S. V. Gusev,A. L. Likhtarnikov +1 more
TL;DR: A history of the Kalman-Popov-Yakubovich lemma and the theorem of losslessness of the S-procedure can be found in this article, where a review of the studies directly concerned with these statements are reviewed.
Journal ArticleDOI
The Circle Criterion and Input-to-State Stability
TL;DR: In this article, the authors provide an overview of the circle criterion and its connection with the ISS, which is concerned with the analysis of a feedback interconnection of Lure type, which consists of a linear system in the forward path and a sector bounded nonlinearity in the negative feedback path.
Journal ArticleDOI
Zames-Falb multipliers for absolute stability: from O'Shea's contribution to convex searches
TL;DR: This tutorial paper aims to provide a clear and comprehensive introduction to the topic of absolute stability from a user viewpoint, reviewing the stability theory, the properties of the multipliers (including their phase properties, phase-equivalence results and the issues associated with causality), and convex searches.
References
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Journal ArticleDOI
Quantized feedback stabilization of linear systems
TL;DR: A new control design methodology is proposed, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves, which yields global asymptotic stability.
Book
Stability of nonlinear control systems
TL;DR: In this article, Liapunov and Popov developed a control system as developed from direct method of LAPUNOV, noting V. M. Popov's contribution.
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Frequency-Domain Methods for Nonlinear Analysis: Theory and Applications
TL;DR: Classical absolute stability theory dichotomy and stability of equilibria sets cycles, homoclinic and heterocliatic trajectories are discussed in this article. But the relative stability of these trajectories is unknown.
Journal ArticleDOI
Absolute stability, conditional stability and bifurcation in Kolmogrov-type predator-prey systems with discrete delays
TL;DR: In this article, the authors consider three classes of Kolmogorov-type predator-prey systems with discrete delays and study absolute stability, conditional stability and bifurcation of these systems from a global point of view on both the parameters and delays.