A characterization of the positivity of a discrete quadratic functional with mixed state endpoints is presented. The functional is transformed in two different ways into problems with separable endpoints to which previous results are applied. The outcome are conditions that include augmented conjoined bases and implicit and explicit Riccati equations with corresponding augmented equality or inequality boundary conditions. The results of this paper extend and complete known ones.

Last change: September 24, 2002. (c) Roman Hilscher