Controllability of a generalized multi-pantograph system of non-integer order with state delay

Author:

Ahmad Irshad1,Ahmad Saeed1,Rahman Ghaus ur2,De la Sen Manuel3

Affiliation:

1. Department of Mathematics University of Malakand Chakdara, 18800 Dir (L), Khyber Pakhtunkhwa, Pakistan

2. Department of Mathematics, University of Swat, 01923 Swat, Khyber Pakhtunkhwa, Pakistan

3. Department of Electricity and Electronics, Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa 48940- Leioa (Bizkaia), Spain

Abstract

<abstract><p>This paper presents the dynamical aspects of a nonlinear multi-term pantograph-type system of fractional order. Pantograph equations are special differential equations with proportional delays that are employed in many scientific disciplines. The pantograph mechanism, for instance, has been applied in numerous scientific disciplines like electrodynamics, engineering, and control theory. Because of its key rule in diverse fields, the current study establishes some necessary criteria for its controllability. The main idea of the proof is based on converting the system into a fixed point problem and introducing a suitable controllability Gramian matrix $ \mathcal{G}_{c} $. The Gramian matrix $ \mathcal{G}_{c} $ is used to demonstrate the linear system's controllability. Controllability criteria for the associated nonlinear system have been established in the sections that follow using the Schaefer fixed-point theorem and the Arzela-Ascoli theorem, as well as the controllability of the linear system and a few key assumptions. Finally, a computational example is listed.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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