AI Summary & Key Takeaways
AI InsightThe obtained results may be applied in various areas of time scale dynamics, for example, in Stability Theory.
📌 3 Key Takeaways
Abstract
The linear non-homogeneous systems of difference equations on time scales with delta derivatives are studied. 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 of linear time-varying dynamic-algebraic equations. The methods of the paper are constructive: we use the projector approach where the tractability index is just the number of necessary projector. Moreover, we give conditions on coefficients of our system which guarantee the existence of the chain of projectors and makes decoupling possible. This work is a continuation (and a more sophisticated case) of our previous article \cite{SGSK1} where we study equations of index 1. The obtained results may be applied in various areas of time scale dynamics, for example, in Stability Theory.