NDLI: Stability criteria with less LMI variables for linear system with additive time-delays

Content Provider	Springer Nature Link
Author	Ramakrishnan, K. Ray, G.
Copyright Year	2010
Abstract	In this technical note, equivalent stability criterion with minimal number of variables for three recently reported stability criteria is proposed for a class of linear systems with additive time-varying delays. The existing delay-dependent stability criteria for additive time-delay systems have more number of matrix variables in the LMI; and hence, they require more computational cost. The proposed equivalent criteria, unlike the original ones, encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criteria mathematically less complex and computationally more attractive. The complexity involved in the existing stability criteria is attributed to the fact the cross-terms that emanate from the time-derivative of the Lyapunov-Krasovskii functional are dealt with free-weighting matrices. Hence, apart from the matrix variables that are associated in the corresponding Lyapunov-Krasovskii functional, the existing criteria also have additional matrix variables in them. In this paper, we have devised techniques to eliminate the free-weighting matrices in the existing stability criteria without sacrificing the conservatism. The resulting equivalent stability criteria, therefore, have least possible number of variables in the LMI; and hence, have minimum computational burden. The effectiveness of the proposed equivalent criteria is validated on a numerical example.
Starting Page	263
Ending Page	274
Page Count	12
File Format	PDF
ISSN	15985865
Journal	Journal of Applied Mathematics and Computing
Volume Number	36
Issue Number	1-2
e-ISSN	18652085
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-04-29
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Lyapunov-Krasovskii (LK) functional Delay-dependent stability Linear matrix inequality (LMI) Additive time-varying delay Stability criterion Linear systems Lyapunov and other classical stabilities Asymptotic stability Linear transformations, semilinear transformations Linear inequalities Explicit machine computation and programs Mathematics of Computing ApplicationMathematics/Computational Methods of Engineering Computational Mathematics and Numerical Analysis Theory of Computation
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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