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Finite-time stability analysis of fractional differential systems with variable coefficients
Fengrong Zhang1, Deliang Qian2, Changpin Li3
1College of Science, China University of Petroleum (East China), Qingdao 266580, People's Republic of China.
Chaos (Woodbury, N.Y.)
|February 3, 2019
Summary
This study investigates finite-time stability for fractional differential systems with variable coefficients. New theorems provide sufficient conditions for stability in both homogeneous and nonhomogeneous systems, including those with time delays.
Area of Science:
- Mathematics
- Dynamical Systems
- Control Theory
Background:
- Fractional differential equations are increasingly used to model complex systems.
- Understanding the stability of these systems, particularly in finite time, is crucial for their practical application.
- Variable coefficients and time delays introduce significant challenges in stability analysis.
Purpose of the Study:
- To analyze the finite-time stability of fractional differential systems with variable coefficients.
- To extend stability analysis to include both homogeneous and nonhomogeneous cases.
- To address the impact of time delays on system stability.
Main Methods:
- Utilizing established theories of fractional differential equations.
- Developing and applying novel mathematical theorems for stability analysis.
- Investigating systems with and without time delays.
Main Results:
- Three new theorems on finite-time stability were derived.
- Sufficient conditions for finite-time stability were established for homogeneous systems without time delay.
- Sufficient conditions were also determined for homogeneous systems with time delay.
- Finite-time stability conditions were identified for nonhomogeneous systems with time delay.
Conclusions:
- The study provides crucial theoretical advancements in the finite-time stability of fractional differential systems.
- The findings offer practical tools for designing and analyzing complex dynamical systems with delays and variable coefficients.
- This work contributes to the broader understanding of stability in fractional-order systems.
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