Before revision:  We conjecture that if the state X(k) is positive for k less than or equal to N in response to a "distinguished path" v*(k) which we define, then for all admissible paths v(k), positivity of the state  is also guaranteed . The conjectureis supported by theoretical analysis for some special cases and simulations .
After revision:  We conjecture that if the state X(k) is positive for k less than or equal to N in response to a "distinguished path" v*(k) which we define, then for all admissible paths v(k), positivity of the state is also guaranteed for all time. Support for the conjecture, both theoretical and computational, is provided .