On the discrete Riccati equation and its applications to discrete Hamiltonian systems. (English) Zbl 0836.39003
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.
Reviewer: R.Vaillancourt (Ottawa)
MSC:
| 39A10 | Additive difference equations |
| 39A12 | Discrete version of topics in analysis |
| 37J99 | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |
| 93B05 | Controllability |
Keywords:
comparison theorems; discrete Riccati systems; disconjugacy; autonomous systems; discrete Hamiltonian vector difference systems; optimal control; Hamiltonian solution; Riccati equationCitations:
Zbl 0794.39006References:
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