In this paper we survey Reid roundabout theorems for time scale symplectic systems (S). These theorems list equivalent conditions for the positivity and nonnegativity of the quadratic functional $$F associated with (S). The Reid roundabout theorems in this paper do not impose any normality assumption. We also show that Jacobi systems for nonlinear time scale control problems naturally lead to time scale symplectic systems, and that such a system consists of the Hamiltonian equations corresponding to the weak maximum principle for the quadratic functional $$F.

Last change: October 30, 2008. (c) Roman Hilscher