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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Journal ArticleDOI
Global Stability Results for Switched Systems Based on Weak Lyapunov Functions
TL;DR: Stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function are provided, which may have wider applicability than results based on strong LyAPunov functions.
Journal ArticleDOI
Results and perspectives on fault tolerant control for a class of hybrid systems
TL;DR: The readers are provided a survey on the main techniques that can be used to achieve the FTC goals of HS, including FTC for HS with continuous stability goal, and supervisory FTC design via hybrid control techniques.
Proceedings ArticleDOI
Stable haptic interaction with switched virtual environments
S. Mahapatra,Milos Zefran +1 more
TL;DR: It is demonstrated that when the dynamics of the virtual environment during the interaction changes, the approaches using traditional notion of passivity for hybrid systems can be used to design stable interaction strategies for such systems.
Journal ArticleDOI
Hybrid Control of Networked Embedded Systems
Andrea Balluchi,Luca Benvenuti,Sebastian Engell,Tobias Geyer,Karl Henrik Johansson,Françoise Lamnabhi-Lagarrigue,John Lygeros,Manfred Morari,Georgios Papafotiou,Alberto Sangiovanni-Vincentelli,Fortunato Santucci,Olaf Stursberg +11 more
TL;DR: An overview of recent developments in four of the most prominent areas where hybrid control methods have found application: control of power systems, industrial process control, design of automotive electronics and communication networks and language specification problems.
Journal ArticleDOI
Control of a planar underactuated biped on a complete walking cycle
Ahmed Chemori,Antonio Loria +1 more
TL;DR: This work proposes control laws to drive the robot for a finite time during each phase of motion, while ensuring certain robustness vis-a-vis the impacts which are treated as external perturbations.
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).
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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.