Analytical and numerical methods for the stability analysis of linear fractional delay differential equations

Authors:
Eva Kaslik;Seenith Sivasundaram
Affiliations:
Institute e-Austria Timisoara, Bd. V. Parvan nr. 4, room 045B, 300223, Timisoara, Romania and Department of Mathematics and Computer Science, West University of Timisoara, Bd. V. Parvan nr. 4, 300 ...;Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

In this paper, several analytical and numerical approaches are presented for the stability analysis of linear fractional-order delay differential equations. The main focus of interest is asymptotic stability, but bounded-input bounded-output (BIBO) stability is also discussed. The applicability of the Laplace transform method for stability analysis is first investigated, jointly with the corresponding characteristic equation, which is broadly used in BIBO stability analysis. Moreover, it is shown that a different characteristic equation, involving the one-parameter Mittag-Leffler function, may be obtained using the well-known method of steps, which provides a necessary condition for asymptotic stability. Stability criteria based on the Argument Principle are also obtained. The stability regions obtained using the two methods are evaluated numerically and comparison results are presented. Several key problems are highlighted.