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
Exponential stability of impulsive systems with application to uncertain sampled-data systems
TL;DR: A positive constant is found which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed and is applied to the analysis and state-feedback stabilization of nonlinear time-varying impulsive systems.
Book ChapterDOI
Engineering Self-Adaptive Systems through Feedback Loops
Yuriy Brun,Giovanna Di Marzo Serugendo,Cristina Gacek,Holger Giese,Holger M. Kienle,Marin Litoiu,Hausi A. Müller,Mauro Pezzè,Mary Shaw +8 more
TL;DR: The state-of-the-art in engineering self-adaptive systems is explored and the critical challenges the community must address to enable systematic and well-organized engineering of self- Adaptive and self-managing software systems are identified.
Journal ArticleDOI
Stability and Stabilization of Continuous-Time Switched Linear Systems
TL;DR: This paper addresses two strategies for the stabilization of continuous-time, switched linear systems and is designed from the solution of what the authors call Lyapunov-Metzler inequalities from which the stability condition (including chattering) is expressed.
Journal ArticleDOI
Stability, ${l}_{2}$ -Gain and Asynchronous ${H}_{{\infty}}$ Control of Discrete-Time Switched Systems With Average Dwell Time
Lixian Zhang,Peng Shi +1 more
TL;DR: The stability and l 2-gain problems for a class of discrete-time switched systems with average dwell time (ADT) switching are investigated by allowing the Lyapunov-like functions to increase during the running time of subsystems to facilitate the studies on the issue of asynchronous control.
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.
Book
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.