A new non-iterative solution for a class of difference Riccati equations

Recently, two non-iterative solutions for difference Riccati equations (DREs) have been developed employing max-plus primal and dual space fundamental solution semigroups. These solutions provide explicit formulas that allow the non-iterative computation of the DRE solution corresponding to any initial condition in a specific well-defined set. In this paper, a third non-iterative solution to a class of difference Riccati equation is developed. It is shown that this new non-iterative solution avoids some specific drawbacks observed in the two existing max-plus based non-iterative solutions at the expense of a semigroup property.