A Lyapunov approach to the stability of fractional differential equations

By Jean-Claude Trigeassou, N. Maamri, Jocelyn Sabatier, Alain Oustaloup. Signal Processing, 2009

401 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f8f02450166292caf154e73fbf307e725af0a06c

How researchers see this paper

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In Control and Systems Engineering

1. Yiheng Wei
2. Yong Wang
3. Ravi P. Agarwal
4. Yuquan Chen
5. Songsong Cheng
6. Shouming Zhong
7. Chun Yin
8. Donal O'Regan

In Modeling and Simulation

1. Donal O'Regan
2. Ravi P. Agarwal
3. Yiheng Wei
4. Yong Wang
5. Snezhana G. Hristova
6. Shouming Zhong
7. Chun Yin
8. Jun Cheng

In Numerical Analysis

1. Ravi P. Agarwal
2. Donal O'Regan
3. Shouming Zhong
4. Snezhana G. Hristova
5. Chun Yin
6. Yiheng Wei
7. Yuquan Chen
8. Yong Wang

Citations in the corpus

• Completeness on the stability criterion of fractional order LTI systems (2017, methodology): “Similar idea on replacing Pn×n α1 by P n×n 1 has been presented earlier by [24, 5].”
• Adaptive backstepping output feedback control for a class of nonlinear fractional order systems (2016, background): “By means of an advanced stability analysis method, i.e., indirect Lyapunovmethod [20,21] studied fractional order adaptive backstepping control with state feedback.”
• Stability Analysis of a Fractional-Order Linear System Described by the Caputo–Fabrizio Derivative (2019, methodology): “In addition, LMI approach [9–11] and Lyapunov approach [12,13] are also used to investigate the stability of fractional order linear time invariant systems.”
• Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems (2015, background): “2 [30] Let (t) be the impulse response of a linear system.”
• OSCILLATORY BEHAVIOR OF A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH DAMPING (2013, methodology): “Many papers have investigated some aspects of fractional differential equations, such as the existence and uniqueness of solutions to Cauchy type problems, the methods for explicit and numerical solutions, and the stability of solutions, and we refer to [12–19].”
• Fractional order sliding mode control via disturbance observer for a class of fractional order systems with mismatched disturbance, (2018, neutral): “Lately the closed-loop stability is proven via the indirect Lyapunov method [16].”
• A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations (2016, methodology): “As is noted in [40] there are several difficulties encountered when one applies the Lyapunov technique to fractional differential equations.”