NEW RESULTS ON FINITE-TIME STABILITY FOR NONLINEAR FRACTIONAL ORDER LARGE SCALE SYSTEMS  WITH TIME VARYING DELAY AND INTERCONNECTIONS

Phạm Ngọc Anh; Nguyễn Trường Thanh; Hoàng Ngọc Tùng

doi:10.34238/tnu-jst.2020.02.2341

NEW RESULTS ON FINITE-TIME STABILITY FOR NONLINEAR FRACTIONAL ORDER LARGE SCALE SYSTEMS WITH TIME VARYING DELAY AND INTERCONNECTIONS

About this article

Received: 15/11/19 Revised: 27/02/20 Published: 28/02/20

Authors

1. Pham Ngoc Anh, Hanoi University of Mining and Geology, Vietnam
2. Nguyen Truong Thanh , Hanoi University of Mining and Geology, Vietnam
3. Hoang Ngoc Tung, Thang Long University, Hanoi, Vietnam

Abstract

This paper investigates finite-time stability problem of a class of interconnected fractional order large-scale systems with time-varying delays and nonlinear perturbations. Based on a generalized Gronwall inequality, a sufficient condition for finite-time stability of such systems is established in terms of the Mittag-Leffler function. The obtained results are applied to finite-time stability of linear uncertain fractional order large-scale systems with time-varying delays and linear non autonomous fractional order large-scale systems with time-varying delays.

Keywords

Finite-time stability; large-scale systems; fractional order systems; time-varying delays; nonlinear perturbations.

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References

[1]. D. P. Siliak, Large-Scale Dynamic Systems: Stability and Structure. North Holland: Amsterdam, 1978.

[2]. M. Mahmoud, M. Hassen, and M. Darwish, Large-Scale Control Systems: Theories and Techniques. Marcel-Dekker: New York, 1985.

[3]. S. Liu, X. F. Zhou, X. Li, and W. Jiang, “Asymptotical stability of Riemann–Liouville fractional singular systems with multiple time-varying delays,” Appl. Math. Lett., 65, pp. 32-39, 2017.

[4]. R. Rakkiyappan, G. Velmurugan, and J. Cao, “Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays,” Nonlinear Dynam., 78, pp. 2823-2836, 2014.

[5]. S. Liu, X. Y. Li, W. Jiang, and X. F. Zhou, “Mittag-Leffler stability of nonlinear fractional neutral singular systems,” Commun. Nonlinear Sci. Numer. Simul., 17, pp. 3961-3966, 2012.

[6]. M. P. Lazarevic, and D. Lj. Debeljkovic, “Finite-time stability analysis of linear autonomous fractional-order systems with delayed state,” Asian J. Control, 7, pp. 440-447, 2005.

[7]. H. Ye, J. Gao, and Y. Ding, “A generalized Gronwall inequality and its application to a fractional differential equation,” J. Math. Anal. App., 328, pp. 1075-1081, 2007.

[8]. A. A. Kilbas, H. Srivastava and J. Trujillo, Theory and Applications of Fractional Differential Equations. Amsterdam: Elsvier, 2006.

[9]. I. Podlubny, Fractional Differential Equations. Academic Press, San Diego, 1999.

DOI: https://doi.org/10.34238/tnu-jst.2020.02.2341

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