Robustness Analysis of a Type of Iterative Algorithm for R-L Fractional Nonlinear Control Systems in the Sense of L p Norm

Abstract

The paper is concerned with the robustness analysis of a type of iterative algorithm for R-L fractional nonlinear control systems in the sense of $L_p$ norm. Firstly, according to the Laplace transform and M-L function, the concept of mild solutions of the system is derived. Secondly, we give the sufficient conditions of robustness analysis of the $P{D}^{\alpha }$ -type ILC algorithm with uncertain disturbances and then study the robust analysis of the second-order $P{D}^{\alpha }$ -type ILC algorithm. At last, two fractional examples are given to demonstrate the results.