Journal ArticleDOI
Multiple Lyapunov functions and other analysis tools for switched and hybrid systems
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TLDR
Bendixson's theorem is extended to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.Abstract:
We introduce some analysis tools for switched and hybrid systems. We first present work on stability analysis. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability and use iterated function systems theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set. Finally, we extend Bendixson's theorem to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.read more
Citations
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Basic problems in stability and design of switched systems
Daniel Liberzon,A.S. Morse +1 more
TL;DR: In this paper, the authors survey three basic problems regarding stability and design of switched systems, including stability for arbitrary switching sequences, stability for certain useful classes of switching sequences and construction of stabilizing switching sequences.
Journal ArticleDOI
Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results
Hai Lin,Panos J. Antsaklis +1 more
TL;DR: This paper focuses on the stability analysis for switched linear systems under arbitrary switching, and highlights necessary and sufficient conditions for asymptotic stability.
Journal ArticleDOI
Hybrid dynamical systems
TL;DR: In this paper, the authors present a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems and on the basics of hybrid control, focusing on the robustness of asymptotic stability to data perturbation, external disturbances and measurement error.
Journal ArticleDOI
Stabilization of linear systems with limited information
Nicola Elia,Sanjoy K. Mitter +1 more
TL;DR: By relaxing the definition of quadratic stability, it is shown how to construct logarithmic quantizers with only finite number of quantization levels and still achieve practical stability of the closed-loop system.
Journal ArticleDOI
Perspectives and results on the stability and stabilizability of hybrid systems
TL;DR: In this paper, the authors introduce the concept of hybrid systems and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems.
References
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
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TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
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Variable structure systems with sliding modes
TL;DR: Design and analysis forVariable structure systems are surveyed in this paper and it is shown that advantageous properties result from changing structures according to this switching logic.
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Fractals Everywhere
TL;DR: Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section.
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Nonlinear Systems Analysis
TL;DR: In this article, the authors consider non-linear differential equations with unique solutions, and prove the Kalman-Yacubovitch Lemma and the Frobenius Theorem.