Extended matrix pencils for the delta-operator Riccati equation

This paper has introduced an extended matrix pencil problem associated with the solution of the delta-operator (difference operator) algebraic Riccati equation. The result is integrated into a systematic treatment of solution algorithms for differential, shift, and difference operator algebraic Riccati equations. These algorithms included the standard eigenvalue problem for ζ-Hamiltonian matrices, a generalized eigenvalue problems for an associated matrix pencil, and the extended matrix pencil generalized eigenvalue problem. The relevant numerical solution techniques for obtaining the stabilizing solution of the corresponding algebraic Riccati equation from each of these problems were presented, along with a discussion of their relative advantages and disadvantages