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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Book ChapterDOI
Introduction to Hybrid Systems
TL;DR: This chapter provides an introduction to hybrid systems, building them up first from the completely continuous side and then from thecompletely discrete side.
Journal ArticleDOI
Stability and Stabilization of a Class of Multimode Linear Discrete-Time Systems With Polytopic Uncertainties
TL;DR: The construction of multiple parameter-dependent quadratic Lyapunov-like functions is invoked, by which the stability and stabilization conditions are derived and formulated in terms of a set of linear matrix inequalities.
Journal ArticleDOI
Stabilization of a class of stochastic differential equations with Markovian switching
Chenggui Yuan,John Lygeros +1 more
TL;DR: The problem of mean square exponential stabilization for a class of stochastic differential equations with Markovian switching for controllers of this type is studied.
Journal ArticleDOI
A separation principle for linear switching systems and parametrization of all stabilizing controllers
TL;DR: It is shown that, if the necessary and sufficient conditions are satisfied, given any arbitrary family of compensators K i,(s), each one stabilizing the corresponding LTI plant (Ai, Bi, Ci) for fixed i, there exist suitable realizations for each of these compensators, which assure stability under arbitrary switching.
Proceedings ArticleDOI
Output feedback control of switched nonlinear systems using multiple Lyapunov functions
TL;DR: In this article, a hybrid nonlinear output feedback control methodology for a broad class of switched nonlinear systems with input constraints is proposed, where output feedback controllers are synthesized, using a combination of bounded state feedback controllers, high gain observers and appropriate saturation filters, to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain.
References
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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.