On the discrete Riccati equation and its applications to discrete Hamiltonian systems
The authors derive comparison theorems for discrete Riccati systems and sufficient conditions of disconjugacy for such autonomous systems, that is, systems with constant coefficient matrices. Applications are made to discrete Hamiltonian vector difference systems introduced by the authors [Proc. Am. Math. Soc., 119, No. 2, 525-533 (1993; Zbl 0794.39006)]. An application is also made to the existence of an optimal control of discrete Hamiltonian systems and the final discussion is summarized in a conjecture on the existence of a Hamiltonian solution to a Riccati equation.
discrete Hamiltonian vector difference systems
scientific article; zbMATH DE number 796913
scientific article