Journal ArticleDOI
Asymptotic H/sub /spl infin// control of singularly perturbed systems with parametric uncertainties
Peng Shi,Vasile Dragan +1 more
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The authors' attention is focused on the design of a composite linear controller based on the slow and fast problems such that both stability and a prescribed H/sub /spl infin// performance for the full-order system are achieved.Abstract:
This paper deals with the problem of control of singularly perturbed linear continuous-time systems. The authors' attention is focused on the design of a composite linear controller based on the slow and fast problems such that both stability and a prescribed H/sub /spl infin// performance for the full-order system are achieved. The asymptotic behavior of the composite controller is studied, which is independent of the singular perturbation /spl epsiv/ when /spl epsiv/ is sufficiently small. Furthermore, the problem of robust control for the above system with parameter uncertainty is also investigated.read more
Citations
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Singular perturbations and time scales in control theory and applications: An overview
TL;DR: This paper presents an overview of singular perturbations and time scales (SPaTS) in control theory and applications during the period 1984-2001 and is not intended to be an exhaustive survey on the topic.
Journal ArticleDOI
Fuzzy-model-based D-stability and nonfragile control for discrete-time descriptor systems with multiple delays
TL;DR: D-stability criteria are proposed to ensure that all the poles of the descriptor T-S fuzzy system are located within a disk contained in the unit circle, and a sufficient condition is presented such that the closed-loop system is regular, causal, and D-stable, in spite of parameter uncertainties and multiple state delays.
Journal ArticleDOI
A sliding mode approach to stabilization of nonlinear Markovian jump singularly perturbed systems
TL;DR: A mode-dependent fuzzy SMC law is synthesized to induce and maintain the sliding motion despite partly unknown transition probabilities and parameter uncertainties and the developed method is applied to stabilize a modified series DC motor system.
Journal ArticleDOI
Nonfragile $\mathcal{H}_{\infty}$ Control for Fuzzy Markovian Jump Systems Under Fast Sampling Singular Perturbation
TL;DR: In this article, a singular perturbation parameter independent condition is derived to make sure the underlying closed-loop system's stability and a mixed $ √ √ H$ and passive performance simultaneously.
Journal ArticleDOI
H/sub /spl infin// filtering for fuzzy singularly perturbed systems with pole placement constraints: an LMI approach
TL;DR: In this paper, a fuzzy H/sub /spl infin/ controller is proposed for singularly perturbed nonlinear systems, which guarantees that the L/sub 2/gain from an exogenous input to a filter error is less than or equal to a prescribed value.
References
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Journal ArticleDOI
State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
Book
Singular perturbation methods in control : analysis and design
TL;DR: This SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications.
Journal ArticleDOI
Singular perturbations and time-scale methods in control theory: Survey 1976-1983
TL;DR: 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.
Journal ArticleDOI
Simplifying the H∞ theory via loop-shifting, matrix-pencil and descriptor concepts
TL;DR: In this article, the 2-Riccati H∞ controller formulae and derivations are simplified via various loop-shifting transformations that are naturally expressed in terms of a degree-one polynomial system matrix (PSM) closely related to the Luenberger descriptor form of a system.
Journal ArticleDOI
H ∞ -optimal control for singularly perturbed systems. Part I: perfect state measurements
Zigang Pan,Tamer Basar +1 more
TL;DR: It is shown that as the singular perturbation parameter ϵ approaches zero, the optimal disturbance attenuation level for the full-order system under a quadratic performance index converges to a value that is bounded above by the maximum of the optimal disturbances attenuation levels for the slow and fast subsystems under appropriate "slow" and "fast"quadratic cost functions.
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