Iterative learning control for Hilfer-type fractional-order quaternion-valued impulsive systems

Abstract

In this paper, we study quaternion-valued differential equations with impulses, in the sense of the Hilfer fractional derivative, and analyze the convergence behavior of two kinds of iterative learning control strategies: proportional-type and proportional-integral-type. The $\lambda$-norm concepts are used to analyze the convergence behavior, which offers a powerful method for evaluating the accuracy and stability of the solutions. By establishing sufficient conditions, we analyze the effects of the impulsive and fractional-order effects on the convergence of the system, and the paper provides examples to show the theoretical results and the usefulness of the suggested techniques.