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
Asymptotic stability and disturbance attenuation properties for a class of networked control systems
TL;DR: In this article, stability and disturbance attenuation issues for a class of networked control systems (NCSs) under uncertain access delay and packet dropout effects are considered, where the authors formulate such NCSs as a discrete-time switched system.
Proceedings ArticleDOI
LMI design of a switched observer with model uncertainty: Application to a hysteresis mechanical system
TL;DR: A linear matrix inequality (LMI) technique for observer based state estimation of discrete time linear switched systems with uncertainties is developed and sufficient conditions of global convergence of the observer are proposed.
Homogeneous Rational Lyapunov Functions for Performance Analysis of Switched Systems
TL;DR: In this article, a homogeneous rational Lyapunov function (HRLF) was proposed for determining the root mean square (RMS) gain of continuous-time switched linear systems, and sufficient conditions for establishing upper bounds of the sought performance indexes in the case of arbitrary switching were given in terms of linear matrix inequality feasibility tests by searching for an HRLF of chosen degree.
Proceedings ArticleDOI
On Several Composite Quadratic Lyapunov Functions for Switched Systems
Tingshu Hu,Liqiang Ma,Zongli Lin +2 more
TL;DR: It is observed that the min of quadratics, which is nondifferentiable and nonconvex, may be a more convenient tool than the other two types of functions which are convex and/or differentiable.
Journal ArticleDOI
On absolute stability of one class of nonlinear switched systems
TL;DR: In this article, the authors considered a class of nonlinear switched systems and proposed methods of developing Lyapynov functions for the systems under study, in the fulfillment of which the asymptotic stability of the zero solution will take place for any witching laws and for any admissible nonlinearities entering into right sides of the equations under discussion.
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.