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

• Authors: Farshad Merrikh-Bayat
• 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.

Keywords

EN

fractional-delay system; stability testing; Riemann surface; Rouche’s theorem; simulation

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 6
• Pages: 855-862

Dates

published

1 - 6 - 2013

online

9 - 10 - 2013

Contributors

author

Farshad Merrikh-Bayat

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

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Identifiers

DOI

10.2478/s11534-013-0226-0