Linear Time-Varying Dynamic-Algebraic Equations of Index $\geq 2$ on Time Scales

TL;DR

This paper introduces a new class of linear time-varying dynamic-algebraic equations of index greater than or equal to 2 on arbitrary time scales, along with a decoupling procedure using a projector approach.

Contribution

It extends previous work on index 1 equations to higher index equations and proposes a decoupling method for these complex systems.

Findings

Decoupling procedure effectively separates the equations.

Applicable to arbitrary time scales.

Extends theoretical understanding of dynamic-algebraic equations.

Abstract

In this paper, we introduce a class of linear time-varying dynamic-algebraic equations(LTVDAE) of tractability index $\geq 2$ on arbitrary time scales. We propose a procedure for the decoupling of the considered class LTVDAE. In the paper is used a projector approach. This work is a continuation of our previous article where we study equations of index 1.