Existence theorem for the difference Riccati equations

摘要

To obtain a necessary and sufficient condition for the existence of a solution of discrete Riccati equations, a new approach is proposed, and an interesting relation between the equilibrium points of Riccati equations and the existence of the solution is shown. The results can be applied to nonsymmetric Riccati equations. However, the results in this paper do not improve our resources for the optimal-control problem or filtering problem, though, roughly speaking, the known results on those problems are included.