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
Contact stability analysis of a one degree-of-freedom robot using hybrid system stability theory
Zoe Doulgeri,George Iliadis +1 more
TL;DR: In this work, the elementary task of controlling the contact of a one degree-of-freedom (dof) robot with a compliant surface is modeled as a switched system and conditions on feedback gains are derived that guarantee Lyapunov stability of the hybrid task.
Proceedings ArticleDOI
Maximally secure mitigation of protection misoperations in power systems
N. Eva Wu,Qiu Qin,Mustafa Salman +2 more
TL;DR: The processes of misoperations and their mitigation into a scalable stochastic discrete-state model are introduced and a mitigation strategy is developed to minimize the risk of cascading failures.
Proceedings ArticleDOI
Stabilizing linear time-invariant systems with finite-state hybrid static output feedback
Guisheng Zhai,Xinkai Chen +1 more
TL;DR: This work considers a hybrid control strategy composed of a finite set of static output feedback controllers and a switching law so that the closed-loop system is asymptotically stable when the controllers are switched under the switching law.
Proceedings ArticleDOI
L/sub 2/ gain analysis for switched systems with continuous-time and discrete-time subsystems
TL;DR: In this article, the authors considered the case where a common Lyapunov function exists for all subsystems in L/sub 2/ sense, and showed that the switched system has the same level /spl gamma/ under arbitrary switching.
Proceedings ArticleDOI
Design of Switched Linear Systems in the Presence of Actuator Saturation
Liang Lv,Zongli Lin,C.L. Brown +2 more
TL;DR: In this article, the authors formulate the problem of designing a switching scheme for a group of linear systems as a constrained optimization problem with the objective of maximizing an estimate of the domain of attraction.
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.