Regular Papers

International Journal of Control, Automation and Systems 2020; 18(4): 1002-1011

Published online November 28, 2019

https://doi.org/10.1007/s12555-018-0688-3

© The International Journal of Control, Automation, and Systems

Study on Asymptotic Stability of Fractional Singular Systems with Time Delay

Dazi Li*, Liming Wei, Tianheng Song, and Qibing Jin

Beijing University of Chemical Technology

Abstract

The stability of fractional singular systems with time delay is discussed. Considering the singularity of the system, a system is decomposed into two subsystems. Through fractional Laplacian transformation and inverse Laplacian transformation on the subsystems, the expression of the state variables in time domain is obtained. According to the characteristics of Mittag-Leffler function, some inequalities that have important influence on stability are derived. Finally, a new sufficient condition is found to make the fractional singular systems with time delay asymptotically stable when the fractional order belongs to1 < α < 2. Meanwhile, the sufficient condition is also obtained to make the system stable under the nonlinear disturbance. All processes are proved and numerical examples are provided to show the validity and feasibility of the proposed method.

Keywords Fractional Laplacian inverse transform, fractional Laplacian transform, fractional singular systems, nonlinear disturbance, stability, time delay.

Article

Regular Papers

International Journal of Control, Automation and Systems 2020; 18(4): 1002-1011

Published online April 1, 2020 https://doi.org/10.1007/s12555-018-0688-3

Copyright © The International Journal of Control, Automation, and Systems.

Study on Asymptotic Stability of Fractional Singular Systems with Time Delay

Dazi Li*, Liming Wei, Tianheng Song, and Qibing Jin

Beijing University of Chemical Technology

Abstract

The stability of fractional singular systems with time delay is discussed. Considering the singularity of the system, a system is decomposed into two subsystems. Through fractional Laplacian transformation and inverse Laplacian transformation on the subsystems, the expression of the state variables in time domain is obtained. According to the characteristics of Mittag-Leffler function, some inequalities that have important influence on stability are derived. Finally, a new sufficient condition is found to make the fractional singular systems with time delay asymptotically stable when the fractional order belongs to1 < α < 2. Meanwhile, the sufficient condition is also obtained to make the system stable under the nonlinear disturbance. All processes are proved and numerical examples are provided to show the validity and feasibility of the proposed method.

Keywords: Fractional Laplacian inverse transform, fractional Laplacian transform, fractional singular systems, nonlinear disturbance, stability, time delay.

IJCAS
May 2024

Vol. 22, No. 5, pp. 1461~1759

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