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
Fixed-time stability of switched systems with application to a problem of formation control
TL;DR: With the aid of the multiple Lyapunov function method, constraints on switching signals are derived under which global fixed-time stability of zero solutions of considered systems can be guaranteed.
Proceedings ArticleDOI
Optimal switching control design for polynomial systems: an LMI approach
TL;DR: A new LMI approach to the design of optimal switching sequences for polynomial dynamical systems with state constraints has a guarantee of global optimality, in the sense that an asympotically converging hierarchy of lower bounds on the achievable performance is obtained.
Proceedings ArticleDOI
Stability and stabilization of switched linear discrete-time systems with polytopic uncertainties
TL;DR: In this article, a switched parameter-dependent quadratic Lyapunov function is proposed, by which the stability conditions are derived and formulated in terms of a set of linear matrix inequalities.
Journal ArticleDOI
Analysis of switched normal discrete-time systems
TL;DR: In this paper, the stability and L 2 gain properties for a class of switched systems which are composed of normal discrete-time subsystems were studied and it was shown that a common quadratic Lyapunov function exists for all subsystems and that the switched normal system is exponentially stable under arbitrary switching.
Journal ArticleDOI
Hybrid stabilization and synchronization of nonlinear systems with unbounded delays
Xinzhi Liu,Peter Stechlinski +1 more
TL;DR: The theoretical results provide insight into how hybrid control strategies can be constructed to synchronize a class of nonlinear systems with unbounded delay through hybrid control through numerical simulations.
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.