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
More filters
Journal ArticleDOI
Stability of Dynamical Systems with Discontinuous Motions
Anthony N. Michel,Ling Hou +1 more
TL;DR: In this paper, a stability theory for discontinuous dynamical systems (DDS) is presented, i.e. continuous-time systems whose motions are not necessarily continuous with respect to time.
Journal ArticleDOI
Finite-time stability and asynchronously switching control for a class of time-varying switched nonlinear systems:
TL;DR: It is found that related results on autonomous switched nonlinear systems cannot be simply extended to non-autonomous systems and a sufficient condition has been proposed for this class of systems using the average dwell time method.
Dissertation
Stabilisation robuste des systèmes affines commutés. Application aux convertisseurs de puissance
TL;DR: In this article, the authors consider a set of strategies de commutations echantillonnees construite a partir d'une fonction de commande de Lyapunov en temps continu, nous cherchons a determiner the region de l'espace dans laquelle converge asymptotiquement l'ensemble des trajectoires du systeme.
Stability Analysis and Stabilization for Bimodal Piecewise Linear Systems Based on Eigenvalue Loci
Yasushi Iwatani,Shinji Hara +1 more
TL;DR: In this article, the authors consider convergence and stability analysis for a class of bimodal piecewise linear systems, and derive necessary and sufficient conditions for the planar BLE systems to be stable.
Proceedings ArticleDOI
A Switched Optimized Approach for Road-Departure Avoidance
TL;DR: A control for vehicle steering assistance has been developed to help the driver keep the lane during inattention periods and the designed control has been obtained as a result of a LMI convex optimization problem.
References
More filters
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.