A new approach for second‐order linear matrix descriptor differential equations of Apostol–Kolodner type

Abstract

In this paper, we study a class of linear second‐order matrix descriptor differential equations of Apostol–Kolodner type with constant coefficients. In the new approach, we propose a different transformation from what Kalogeropoulos et al. (2009) have used in their recent paper. However, similarly with them, the Weierstrass canonical form has been considered, and the analytical formula for the solution of this general class is derived naturally for consistent initial conditions. Copyright © 2013 John Wiley & Sons, Ltd.

Linear backward stochastic differential systems of descriptor type with structure and applications to engineering

“…These systems are derived from the linearization process of higher order nonlinear systems in mechanical engineering, and the singular mass matrix is constant as it has been discussed above, see also about the transformation of high order linear descriptor systems to first order [23,31,35] and references therein. Thus, the final value problem (backward case) is proposed and examined.…”

“…(2.1) becomes an ordinary differential equation of descriptor type For readers' convenience, and in order to understand further the strict notation which follows in Section 3 and afterward, in this preliminary section we present briefly some necessary elements about the Thompson canonical form for regular matrix pencils with symmetric and skew-symmetric matrices, i.e. σ α − type, see [18,24,34,35]. Lemma 1.…”

Modeling, reachability and observability of linear multivariable discrete time systems

“…where x(k) ∶ N → R r is the state (or semistate) of the system, u(k) ∶ N → R m is the input of the system, y(k) ∶ N → R p its output and E, A ∈ R r×r , B ∈ R r×m , C ∈ R p×r . [14-16, 19, 65], as well as other applications in economy [70,76], biology [70][71][72], electrical circuit networks [96], engineering [2,11,51,93,94,99,112], social sciences and medicine for positive systems [44] or 2D systems [45].…”

“…where [15], as well as other applications in biology [72] engineering [2,11,51,93,99], social sciences and medicine for positive systems [44] or 2D systems [45].…”

“…Another approach is to first transform the higher order system into a state-space or descriptor system, as in [6,58,64,78]. The descriptor system can then be further decomposed using the Weierstrass decomposition of the matrix pencil involved, into multiple subsystems, which can then be studied separately, as in [20,51,99].…”