Publication details

Implicit Riccati equations and quadratic functionals for discrete symplectic systems



Year of publication 2006
Type Article in Periodical
Magazine / Source International Journal of Difference Equations
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Discrete symplectic system; Quadratic functional; Nonnegativity; Positivity; Riccati inequality; Riccati equation; Conjoined basis; Sturmian theorem
Description 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.
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