Journal ArticleDOI
Basic problems in stability and design of switched systems
Daniel Liberzon,A.S. Morse +1 more
TLDR
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.Abstract:
By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.read more
Citations
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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
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.
Journal ArticleDOI
Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach
TL;DR: The approach followed in this paper looks at the existence of a switched quadratic Lyapunov function to check asymptotic stability of the switched system under consideration and shows that the second condition is, in this case, less conservative.
Proceedings ArticleDOI
Modeling and performance analysis of BitTorrent-like peer-to-peer networks
Dongyu Qiu,R. Srikant +1 more
TL;DR: This paper presents a simple fluid model and considers the built-in incentive mechanism of BitTorrent and its effect on network performance, and provides numerical results based on both simulations and real traces obtained from the Internet.
References
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Book
Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Journal ArticleDOI
Multiple Lyapunov functions and other analysis tools for switched and hybrid systems
TL;DR: Bendixson's theorem is extended to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.
Asymptotic stability and feedback stabilization
TL;DR: In this paper, the authors considered the problem of determining when there exists a smooth function u(x) such that x = xo is an equilibrium point which is asymptotically stable.
Proceedings ArticleDOI
Stability of switched systems with average dwell-time
Joao P. Hespanha,A.S. Morse +1 more
TL;DR: In this article, it was shown that scale-independent hysteresis can produce switching that is slow-on-the-average and therefore the results mentioned above can be used to study the stability of adaptive control systems.
Stability of Switched Systems with Average Dwell-Time 1
P. Hespanha,A. Stephen Morse +1 more
TL;DR: In this article, it was shown that switching among stable linear systems results in a stable system provided that switching is slow-on-the-average, i.e., the number of switches in any nite interval grows linearly with the length of the interval, and the growth rate is suciently small.