Singular perturbations and time-scale methods in control theory: Survey 1976-1983
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TLDR
The survey is aimed at engineers and applied mathematicians interested in model-order reduction, separation of time scales and allied simplified methods of control system analysis and design.About:
This article is published in Automatica.The article was published on 1984-05-01 and is currently open access. It has received 539 citations till now. The article focuses on the topics: Singular perturbation.read more
Citations
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Sliding order and sliding accuracy in sliding mode control
TL;DR: It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay and a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced.
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Higher order sliding modes
TL;DR: So-called sliding modes are introduced, which become main operation modes in the variable structure systems (VSS) and reveal their main drawback: the so-called chattering effect, i.e., dangerous high-frequency vibrations of the controlled system.
Journal ArticleDOI
A robust direct adaptive controller
TL;DR: In this paper, the authors proposed a direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics, which guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions.
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The peaking phenomenon and the global stabilization of nonlinear systems
TL;DR: In this paper, the authors considered the problem of global stabilization for a class of cascade systems, where the first part of the cascade is a linear controllable system and the second part is a nonlinear system receiving the inputs from the states of the first one.
Proceedings ArticleDOI
Singular perturbation approximation of balanced systems
Yang Liu,Brian D. O. Anderson +1 more
TL;DR: The singular perturbation approximation technique for model reduction is related to the direct truncation technique if the system model to be reduced is stable, minimal, and internally balanced as mentioned in this paper.
References
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Variable structure systems with sliding modes
TL;DR: Design and analysis forVariable structure systems are surveyed in this paper and it is shown that advantageous properties result from changing structures according to this switching logic.
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Asymptotic Analysis of Periodic Structures
Book
Asymptotic analysis for periodic structures
TL;DR: In this article, the authors give a systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate.
Book
Geometrical Methods in the Theory of Ordinary Differential Equations
TL;DR: In the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has Since the author explains basic ideas free from a number of 2nd order odes as discussed by the authors.
Book
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.