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Further results on Ulam stability for a system of first-order nonsingular delay differential equations

Zada Akbar, Pervaiz Bakhtawar, Alzabut Jehad, Shah Syed Omar

Demonstratio Mathematica

2020

Vol. 53, nr 1

225--235

This paper is concerned with a system governed by nonsingular delay differential equations. We study the β-Ulam-type stability of the mentioned system. The investigations are carried out over compact and unbounded intervals. Before proceeding to the main results, we convert the system into an equivalent integral equation and then establish an existence theorem for the addressed system. To justify the application of the reported results, an example along with graphical representation is illustrated at the end of the paper.

Linear Repetitive Process Control Theory Applied to a Physical Example

Gałkowski K., Rogers E., Paszke W., Owens D. H.

International Journal of Applied Mathematics and Computer Science

2003

Vol. 13, no 1

87-99

In the case of linear dynamics, repetitive processes are a distinct class of 2D linear systems with uses in areas ranging from long-wall coal cutting and metal rolling operations to iterative learning control schemes. The main feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them for onward translation into efficient routinely applicable controller design algorithms for applications domains. In this paper, we introduce the dynamics of these processes by outlining the development of models for various metal rolling operations. These models are then used to illustrate some recent results on the development of a comprehensive control theory for these processes.