General Response Formula for CFD Pseudo-Fractional 2D Continuous Linear Systems Described by the Roesser Model

Abstract

In many engineering problems associated with various physical phenomena, there occurs a necessity of analysis of signals that are described by multidimensional functions of more than one variable such as time t or space coordinates x, y, z. Therefore, in such cases, we should consider dynamical models of two or more dimensions. In this paper, a new two-dimensional (2D) model described by the Roesser type of state-space equations will be considered. In the introduced model, partial differential operators described by the Conformable Fractional Derivative (CFD) definition with respect to the first (horizontal) and second (vertical) variables will be applied. For the model under consideration, the general response formula is derived using the inverse fractional Laplace method. Next, the properties of the solution will be considered. Usefulness of the general response formula will be discussed and illustrated by a numerical example.

Finite difference based iterative learning control with initial state learning for a class of fractional order two‐dimensional continuous‐discrete linear systems

“…Definition 2 (36). The fractional 𝛼 i -order partial derivative of a 2D continuous function f (t 1 , t 2 ) with respect to variable t i (i = 1, 2) is given by the formula…”

New stability tests for fractional positive descriptor linear systems

“…Descriptor positive systems have been analyzed in [3,8,10] and descriptor fractional linear systems in [6,7,10,18,19]. The two-dimensional continuous CFD pseudo-fractional systems described by the Roesser model have been considered in [15]. The stability of fractional linear discrete-time systems has been investigated in [10,16,17].…”

Shuffle algorithm for fractional descriptor Roesser type continuous-time linear systems

“…The positive linear systems have been introduced and analysed in [9,14,18,22]. The positive fractional linear systems have been investigated in [3,[17][18][19][20]28]. Stability and stabilization of fractional linear systems has been investigated in the papers [3,18,22,30].…”

“…The notion of practical stability of positive fractional discrete-time linear systems has been introduced in [18]. General response formula for CFD -fractional 2D continues linear systems described by the Roesser model is given in [28]. Some recent interesting results in fractional systems theory and its applications can be found in [18,21,28,29].…”

“…General response formula for CFD -fractional 2D continues linear systems described by the Roesser model is given in [28]. Some recent interesting results in fractional systems theory and its applications can be found in [18,21,28,29]. The descriptor linear systems have been analysed by the use of the shuffle algorithm have been analysed in [24][25][26]15].…”