Parameterized linear matrix inequality techniques in fuzzy control system design

Tuan, Hoang Duong; Apkarian, Pierre; Narikiyo, Tatsuo; Yamamoto, Yoshinori

doi:10.1109/91.919253

Cited by 1,043 publications

(395 citation statements)

References 18 publications

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“…proof: Noticing that F (δ) ≥ 0 is equivalent to (14) if X = −I, the result follows easily from the application of the Full Block S-Procedure (theorem 4) in the RSDP (9). QED.…”

Section: Complete Family Of Parametrized Relaxationsmentioning

confidence: 92%

“…Although the determination of all such matrices is not a trivial problem, it is a lot easier than (14) and it is current subject of intensive research. Further information on possible choices of the matrix P can be found in [17].…”

Section: Complete Family Of Parametrized Relaxationsmentioning

confidence: 99%

“…The probabilistic approach, which yields outstanding results on the separability problem, will be reported elsewhere. As a first example of such relaxations, consider the following adaptation of [14]:…”

Section: Corollarymentioning

confidence: 99%

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Robust semidefinite programming approach to the separability problem

Brandão

Vianna

2004

Phys. Rev. A

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“…proof: Noticing that F (δ) ≥ 0 is equivalent to (14) if X = −I, the result follows easily from the application of the Full Block S-Procedure (theorem 4) in the RSDP (9). QED.…”

Section: Complete Family Of Parametrized Relaxationsmentioning

confidence: 92%

Section: Complete Family Of Parametrized Relaxationsmentioning

confidence: 99%

See 1 more Smart Citation

Robust semidefinite programming approach to the separability problem

Brandão

Vianna

2004

Phys. Rev. A

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“…Improvements have appeared in piecewise/gridpoint approaches [37,38], non-PDC design [39,40,41], multi-step non-monotonic Lyapunov functions [42], and LinearFractional transformation approaches to fuzzy modelling [27], with clear links to the LPV gain-scheduling concepts [18]. Widely used relaxations of the double-summation problem (which apply to many fuzzy results) appeared in [43,44], although conservatism remained.…”

Section: Model-based Fuzzy Control Designmentioning

confidence: 99%

Fuzzy control turns 50: 10 years later

Guerra

Sala

Tanaka

2015

Fuzzy Sets and Systems

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In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.

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“…considering i and j as fixed, so that, if (47), (48) hold, then (considering the analogous formulas to (16) and (17)):…”

Section: Where Y Is a Rank-(2p) Tensor (Hence Y Ij Is A Matrix)mentioning

confidence: 99%

Relaxed LMI conditions for closed-loop fuzzy systems with tensor-product structure

Ariño

Sala

2007

Engineering Applications of Artificial Intelligence

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Current fuzzy control research tries to obtain the less conservative conditions to prove stability and performance of fuzzy control systems. In many fuzzy models, membership functions with multiple arguments are defined as the product of simpler ones, where all possible combinations of such products conform a fuzzy partition. In particular, such situation arises with widely-used fuzzy modelling techniques for non-linear systems. These type of fuzzy models will be denoted as tensor-product fuzzy systems, because its expressions can be understood as operations on multi-dimensional arrays. This paper discusses the generalisation to tensor-product fuzzy systems of the results in [5,18]. The procedures here will allow to set up LMI conditions which are less conservative than the cited ones, by exploiting the tensor-product structure of the membership functions. A numerical example illustrates the achieved improvement.

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Parameterized linear matrix inequality techniques in fuzzy control system design

Cited by 1,043 publications

References 18 publications

Robust semidefinite programming approach to the separability problem

Robust semidefinite programming approach to the separability problem

Fuzzy control turns 50: 10 years later

Relaxed LMI conditions for closed-loop fuzzy systems with tensor-product structure

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