General conformable estimators with finite-time stability

Abstract

In this paper, some estimators are proposed for nonlinear dynamical systems with the general conformable derivative. In order to analyze the stability of these estimators, some Lyapunov-like theorems are presented, taking into account finite-time stability. Thus, to prove these theorems, a stability function is defined based on the general conformable operator, which implies exponential stability. The performance of the estimators is assessed by means of numerical simulations. Furthermore, a comparison is made between the results obtained with the integer, fractional, and general conformable derivatives.

Mathematical model to estimate volumetric oxygen transfer coefficient in bioreactors using conformable calculus

“…More recently in (Khalil et al, 2014), the first conformable calculus was introduced that is an alternative to conformal calculus, but with local operators, without memory. These conformable operators can improve the performance of conformal operators for example (see Meléndez-Vázquez et al, 2021;Reyes-Luis et al, 2021;Meléndez-Vázquez et al, 2020), since these operators can introduce a function that conformal operators cannot, regardless of the non-integer order of these derivatives.…”

On the Barbalat lemma extension for the generalized conformable fractional integrals: Application to adaptive observer design

“…There has been a lot of research and description done on it, and we recommend the following references to the readers [17–22]. After that, a new extension for the conformable fractional derivative is described; see previous studies [23–25]. Indeed, the authors demonstrated the solution's uniqueness and its continuous dependency on the source function and initial‐boundary conditions in Li et al [23].…”