On Null Controllability of Nonlinear Neutral-Type Fractional-Order Differential Systems with State Delays and Distributed Delays in the Control, and Impulsive Effects

Authors : Paul Anaetodike Oraekie; Chukwuma Uzoma Okele

Volume/Issue : Volume 8 - 2023, Issue 9 - September

Google Scholar : https://tinyurl.com/2tby9ku9

Scribd : https://tinyurl.com/zdcxch8x

DOI : https://doi.org/10.5281/zenodo.8437449

In this work, Nonlinear Neutral Type Fractional Order Differential Systems with State Delays and Distributed Delays in the Control and Impulsive Effects in Banach Space is presented for Controllability analysis. From the analysis, we established that the System is Null Controllable, and a set of necessary and sufficient conditions for such systems to be Null Controllable were established. Uses were made of the uniformly asymptotically Stability of its Linear Free Base System and the Properness of its Linear Control Base System. We also established that the System admits the Solution pair (x, u) and hence the form of the null control of the system was obtained, using the Riesz theorem and Schauder’s Fixed Point theorem.

Keywords : Null Controllability, Asymptotically Stability, Properness, Controllability, Orthogonality.


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