This paper focuses on developing new Riccati-type conditions for an abnormal time scale symplectic system (S). These conditions provide characterizations of the nonnegativity (with and without a certain ``image condition'') and positivity of the quadratic functionals associated with such a system. The novelty of these conditions rely on the natural conjoined basis $($X_a,U_a) of (S) in which $$X_a(t) is not necessarily invertible, and thus the system (S) could be abnormal. These results are new even in the special case of continuous time, as are some of them in the discrete time setting.

Last change: October 10, 2007. (c) Roman Hilscher