Lyapunov functions for fractional order systems

By N. Aguila-Camacho, Manuel A. Duarte-Mermoud, J. Gallegos. Communications in nonlinear science & numerical simulation, 2014

1,378 citations recorded by the source corpus.

Abstract A new lemma for the Caputo fractional derivatives, when 0 α 1 , is proposed in this paper. This result has proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the stability of many fractional order systems, which can be nonlinear and time varying.

Subfields: Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/78f279fd3dce0cf2635ff81a4939e81a251c1cd9

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In Control and Systems Engineering

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Citations in the corpus

A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations (2016, background): “The main condition concerns the Caputo fractional derivative of the Lyapunov function 0 D q tV (t, x(t)), where x(t) is a solution of the studied fractional equation (see, for example, the papers [8], [19], [23], [31], [32]).”
Adaptive backstepping output feedback control for a class of nonlinear fractional order systems (2016, methodology): “Although the stability of the closed-loop system was analyzed using the direct Lyapunov method [18,19] or final value theorem, both of them show significant conservatism.”
Adaptive Fuzzy Backstepping Control of Fractional-Order Nonlinear Systems (2017, background): “Lemma 5 [3]: If x(t) is a smooth function, then”
On asymptotic properties of solutions to fractional differential equations (2018, neutral): “We list here some typical contributions [1, 7, 2, 14, 21, 22, 15, 34, 36].”
Asymptotical stability of Riemann–Liouville fractional nonlinear systems (2016, methodology): “Very recently, several new inequalities [19,20] on Caputo fractional derivatives of quadratic functions present a very efficient method to analyze stability.”
Lyapunov functions for fractional-order systems in biology: Methods and applications (2020, background): “1 and Lemma 1 of [2], we obtain that C t0 D t L(u(t)) = C t0 D t V (u(t)) + C t0 D t Q(u(t)) ≤ n”