Sentence examples for a singular system of from inspiring English sources

In this article, we study the boundary value problem of a class of a singular system of fractional nabla difference equations whose coefficients are constant matrices.

We first look at the unstructured model; this yields a singular system of ordinary differential equations having interesting dynamical features, such as finite time extinction or persistence of populations.

We know from Lemma 1 that there exists a singular value expansion for H 11, so let (left {sigma _{11}^{ k)}, U_{11}^{ k)}, V_{11}^{ k)}right }_{k=1}^{infty }) be a singular system for the operator (mathsf {H}_{11}: mathcal {T}_{1}rightarrow mathcal {R}_{1}) (see Lemma 5 in Appendix B for the definition of a singular system).

Property 3 follows from the first two properties: The compactness of H ij, established in Property 1, implies the existence of a singular system, since there exists a singular system for any compact operator (see Section 16.1 of [32]).

In the following, we present the first equivalent form (FE1) of system (1.1) by the coordinate transformation, which is also called the standard decomposition of a singular system.

Singular systems have extensive applications in electrical circuits, power systems, economics and other areas, so the filtering of a singular system is especially important and has been extensively studied [5, 6].

In order to proceed with the main result on exponentially practical stability in the pth-moment of a singular system with delay and disturbance (2.1), we make the following assumption; an explanation for this assumption is given in Remark 3.2.

Consider the singular system (3) and the corresponding singular system of the form (41).

Those difficulties are found in an iteration process that contains a near-singular system of equations.

These expressions are calculated as a non-singular system of linear algebraic equations and depend on various parameters involved in this non-singular system.

These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system.