Journal ArticleDOI
Perspectives and results on the stability and stabilizability of hybrid systems
R.A. Decarlo,Michael S. Branicky,Stefan Pettersson,Bengt Lennartson +3 more
- Vol. 88, Iss: 7, pp 1069-1082
TLDR
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.Abstract:
This paper introduces the concept of a hybrid system 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. In this endeavour, this paper surveys the major results in the (Lyapunov) stability of finite-dimensional hybrid systems and then discusses the stronger, more specialized results of switched linear (stable and unstable) systems. A section detailing how some of the results can be formulated as linear matrix inequalities is given. Stability analyses on the regulation of the angle of attack of an aircraft and on the PI control of a vehicle with an automatic transmission are given. Other examples are included to illustrate various results in this paper.read more
Citations
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Proceedings ArticleDOI
Finite-time stability analysis for switched linear systems
TL;DR: It is proved that finite-time boundness is related to both subsystems and switching signal and it is shown that the more information about the signal is known, the less conservative results can be derived.
Journal ArticleDOI
Robotic Manipulators State Observation Via One-Time Gain Switching
TL;DR: New switching-gain observer designs that capitalize on the benefits of low-gain, high- gain, and sliding mode observations are presented and are applied to flexible-joint manipulators in order to explore their performance capabilities.
Structural stability of hybrid systems
TL;DR: It is shown that a Zeno state is locally structurally stable and that a standard equilibrium on the boundary of a domain implies structural instability.
Journal ArticleDOI
Stability analysis of some classes of nonlinear switched systems with time delay
TL;DR: Stability of certain classes of nonlinear time-delay switched systems is studied and the fulfilment of common Lyapunov–Razumikhin functions provides the asymptotic stability of the zero solutions of the considered hybrid systems for any switching law and for any nonnegative delay.
Proceedings ArticleDOI
Structural stability of hybrid systems 1
TL;DR: It is shown that a Zeno state is locally structurally stable and that a standard equilibrium on the boundary of a domain implies structural instability.
References
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Book
Applied Nonlinear Control
TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
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.
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Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.