A remark on discrete quadratic functionals with separable endpoints

摘要

dA characterization of the positivity of a discrete quadratic functional with separable state endpoint constraints is presented in terms of conjugate intervals to 0, various conjoined bases of the associated linear Hamiltonian difference system, and solutions of the implicit and explicit Riccati difference equations. The boundary conditions are in the form of either equalities or (strict) inequalities. Three sets of results are derived under different underlying assumptions.