Implicit Riccati equations and quadratic functionals for discrete symplectic systems
|Year of publication
|Article in Periodical
|Magazine / Source
|International Journal of Difference Equations
|MU Faculty or unit
|Discrete symplectic system; Quadratic functional; Nonnegativity; Positivity; Riccati inequality; Riccati equation; Conjoined basis; Sturmian theorem
|In this paper we study discrete (implicit) Riccati matrix equations associated with discrete symplectic systems and related quadratic functionals F with variable endpoints. We derive these Riccati equations for nonnegative functionals F with separable and jointly varying endpoints. The result for jointly varying endpoints is in terms of the nonaugmented Riccati operator. The method also allows to simplify implicit Riccati equations known for the positivity of F . Finally, we establish a comparison result (Riccati inequality) for solutions of Riccati equations associated with two discrete symplectic systems.