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
Stability analysis of switched linear systems on non-uniform time domain with unstable subsystems
TL;DR: In this article, the stability analysis of a class of switched linear systems evolving on an arbitrary time domain was studied, which consists of a set of unstable linear continuous-time and unstable linear discrete-time subsystems.
Journal ArticleDOI
Construction of switching sequences for reachability realization of switched impulsive control systems
Zhijian Ji,Gang Feng,Xiaoxia Guo +2 more
TL;DR: In this article, an approach is proposed to design switching sequences so that the reachable subspace of switched impulsive control systems is expressed in terms of the reachability state sets of the designed switching sequences.
Proceedings ArticleDOI
Delay-Dependent Output Feedback Guaranteed Cost Control for Uncertain Discrete-Time Switched Delay Systems
Jianbin Qiu,Gang Feng,Jie Yang +2 more
TL;DR: In this paper, a delay-dependent output feedback guaranteed cost controller design for uncertain discrete-time switched systems with time-varying state delay is investigated, where the uncertainties are assumed to have a structured linear fractional form.
Proceedings ArticleDOI
A Model Predictive Control Framework for Asymptotic Stabilization of Discretized Hybrid Dynamical Systems
TL;DR: A method to obtain numerical solutions to the hybrid optimal control problem, amenable to off-the-shelf optimization solvers, and demonstrate this method on the discretization of a prototypical hybrid system.
Journal ArticleDOI
Stability of discontinuous Cauchy problems in Banach space
A.N. Michel,Ye Sun +1 more
TL;DR: In this paper, the authors present Lyapunov stability results for discontinuous dynamical systems (DDS) determined by differential equations in Banach space or Cauchy problems on abstract spaces.
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.