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Number of results

Journal

2013 | 11 | 6 | 855-862

Article title

General formula for stability testing of linear systems with fractional-delay characteristic equation

Content

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Languages of publication

EN

Abstracts

EN
In some applications (especially in the filed of control theory) the characteristic equation of system contains fractional powers of the Laplace variable s possibly in combination with exponentials of fractional powers of s. The aim of this paper is to propose an easy-to-use and effective formula for bounded-input boundedoutput (BIBO) stability testing of a linear time-invariant system with fractional-delay characteristic equation in the general form of $$\Delta \left( s \right) = P_0 \left( s \right) + \sum\nolimits_{i = 1}^N {P_i \left( s \right)\exp ( - \zeta _i s^{\beta _i } ) = 0}$$, where P
i(s) (i = 0,...,N) are the so-called fractional-order polynomials and ξ
i and β
i are positive real constants. The proposed formula determines the number of the roots of such a characteristic equation in the right half-plane of the first Riemann sheet by applying Rouche’s theorem. Numerical simulations are also presented to confirm the efficiency of the proposed formula.

Publisher

Journal

Year

Volume

11

Issue

6

Pages

855-862

Physical description

Dates

published
1 - 6 - 2013
online
9 - 10 - 2013

Contributors

  • Faculty of Electrical Engineering, University of Zanjan, Zanjan, Iran, P.O.Box 313

References

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Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-013-0226-0
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