A Note on the Dimensions of the Structural Invariant Subspaces of the Discrete-Time Singular Hamiltonian Systems

TL;DR

This paper investigates the dimensions of structural invariant subspaces in discrete-time singular Hamiltonian systems, providing insights that aid in understanding their properties and implications for system trajectories.

Contribution

It offers a detailed analysis of the dimensionality of these subspaces, enhancing theoretical understanding of their structure in singular Hamiltonian systems.

Findings

Dimensionality of invariant subspaces is characterized.

Insights into the features of these subspaces are provided.

Implications for admissible trajectories are discussed.

Abstract

The structural invariant subspaces of the discrete-time singular Hamiltonian system are used in 1] to give an analytic nonrecursive expression of all the admissible trajectories. A deeper insight into the features of these subspaces, particularly focused on the dimensionality issue, is the object of this note.