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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Proceedings ArticleDOI
Synthesis of uniformly ultimate boundedness switching laws for discrete-time uncertain switched linear systems
Hai Lin,Panos J. Antsaklis +1 more
TL;DR: In this paper, the problem of synthesizing switching control laws, which assure that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence, is investigated.
Journal ArticleDOI
Stabilization of a class of discrete-time switched systems via observer-based output feedback
Jiao Li,Yuzhong Liu +1 more
TL;DR: In this paper, an observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule, where the main method used in this note is combining switched Lyapunov function (SLF) method with Finsler's Lemma.
Posted Content
Invariance principles for switched systems with restrictions
TL;DR: This paper presents invariance principles for switched nonlinear systems with otherwise arbitrary compact index sets and derive, by using observability-like notions, some convergence criteria which enable the convergence of solutions of switched systems with restrictions originating from the timing of the switchings.
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.
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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.