Singular perturbations and order reduction in control theory - An overview
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The content of main theorems is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.About:
This article is published in Automatica.The article was published on 1976-03-01 and is currently open access. It has received 892 citations till now. The article focuses on the topics: Model order reduction.read more
Citations
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Sliding mode control design principles and applications to electric drives
TL;DR: The main arguments in favor of sliding-mode control are order reduction, decoupling design procedure, disturbance rejection, insensitivity to parameter variations, and simple implementation by means of power converters.
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A survey of linear singular systems
TL;DR: In this paper, a brief historical review of linear singular systems is presented, followed by a survey of results on their solution and properties, and the frequency domain and time domain approaches are discussed together to sketch an overall picture of the current status of the theory.
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A generalized state-space for singular systems
TL;DR: In this article, a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed, and concepts of controllability and observability are defined for the impulsive modes.
A Survey of Model Reduction Methods for Large-Scale Systems
TL;DR: An overview of model reduction methods and a comparison of the resulting algorithms is presented, finding that the approximation error in the former case behaves better globally in frequency while in the latter case the local behavior is better.
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Trends in large space structure control theory: Fondest hopes, wildest dreams
TL;DR: This paper presents a mathematical framework for discussion of large space structure (LSS) control theory, and current trends in LSS control theory and related topics in general control science are surveyed.
References
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Book
Perturbation Methods
Ali H. Nayfeh,Vimal Singh +1 more
TL;DR: This website becomes a very available place to look for countless perturbation methods sources and sources about the books from countries in the world are provided.
Book
Feedback Systems: Input-output Properties
TL;DR: In this paper, the Bellman-Gronwall Lemma has been applied to the small gain theorem in the context of linear systems and convolutional neural networks, and it has been shown that it can be applied to linear systems.
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Perturbation Methods in Applied Mathematics
TL;DR: In this paper, limit process expansions applied to Ordinary Differential Equations (ODE) are applied to partial differential equations (PDE) in the context of Fluid Mechanics.
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Asymptotic expansions for ordinary differential equations
TL;DR: Asymptotic expansions for ordinary differential equations as discussed by the authors, asymptotics expansions for ODEs, Asymptotically expansion for ordinary DDEs and their derivatives.