Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems

By Manuel A. Duarte-Mermoud, N. Aguila-Camacho, J. Gallegos, R. Castro‐Linares. Communications in nonlinear science & numerical simulation, 2015

739 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/ce0940a120b1607d91c193e924ddb061f80a5b2f

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In Control and Systems Engineering

Citations in the corpus

Stability of Caputo fractional differential equations by Lyapunov functions (2015, methodology): “Using an inequality for any continuous function (for the proof see [1]) and Theorem 1 from the paper [6], one can prove the stability of the zero solution of (6.”
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.”
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.”
Lyapunov functions for fractional-order systems in biology: Methods and applications (2020, background): “[20] generalized the result of [2] to the vector case, in order to prove the stability of fractional-order models with reference adaptive control schemes.”
Stability with respect to part of the variables of nonlinear Caputo fractional differential equations (2018, positive): “Indeed, in [4], authors described an uniform stability for fractional order systems using general quadratic Lyapunov functions.”
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].”
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]).”