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Study on Asymptotic Stability of Fractional Singular Systems with Time Delay

Dazi Li*, Liming Wei, Tianheng Song, and Qibing Jin
International Journal of Control, Automation, and Systems, vol. 18, no. 4, pp.1002-1011, 2020

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.

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

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