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
Brief paper: Optimal exponential feedback stabilization of planar systems
A.A. Zevin,Mark A. Pinsky +1 more
TL;DR: This paper solves the problem of finding an optimal feedback control ensuring the maximal rate of convergence of system solutions to the origin for a general class of planar control systems including switched, bilinear systems and ones described by differential inclusions, etc.
Proceedings ArticleDOI
Supervisory control of a mobile robot for agile motion coordination
TL;DR: A supervisory control framework is developed that orchestrates switching among multiple controllers to track nonsmooth trajectories and the stability of the individual controllers and the internal dynamics are proved.
Journal ArticleDOI
Relaxed Stability Conditions for Switched Systems with Dwell Time
TL;DR: In this article, the authors present asymptotic and input-to-state stability results for switched systems with dwell time in which the switching signal is not arbitrary, but is rather chosen as part of the control design strategy.
Switching Controllers: Realization, Initialization and Stability
TL;DR: A general Lyapunov theory is developed for analyzing stability of reset switching systems and the theory is then applied to the problem of synthesizing controller reset relations such that stability is guaranteed under arbitrary switching.
Journal ArticleDOI
Observer design for a class of switched nonlinear systems
Zhengrong Xiang,Weiming Xiang +1 more
TL;DR: An observer design methodology for a class of switched nonlinear systems with Lipschitz nonlinearity where asymptotic observers for each subsystem are developed, and an estimated state updated relation is given to guarantee the convergence of estimated state error for the whole switched non linear systems.
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.