This paper explores the concept of conformable derivative to produce a more general sliding motion, where the speed of convergence can be directly modulated during the design of the conformable operator. Through the analysis of a novel conformable derivative, a newer class of control systems can be proposed, which offer supplementary and entrancing properties to meet broader performance specifications. A conformable integro‐differential sliding motion is enforced in finite‐time, by means of a second‐order sliding mode controller, where the stability at the sliding phase is studied in the Lyapunov framework. Representative simulation examples are provided to show the suitability of the proposed methodology, and an experimental scenario is carried out to evaluate the performance of the proposed scheme under real‐world conditions.
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.
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