Making use of a recently proved Reid Roundabout Theorem for linear Hamiltonian difference systems in the so-called singular case, we derive a Sturm Separation Theorem, a Sturm Comparison Theorem, and a characterization of a discrete quadratic functional being positive definite subject to separated boundary conditions. These results enable us to prove the main theorem of this paper which states the equivalence of positive definiteness of a certain discrete quadratic functional and solvability of some Riccati matrix difference equation together with a certain matrix inequality.

Research Teaching Links Home