On the definition of ‘transfer function’?

The optimal asymptotically stabilizing control problem is formulated, and the theorem for the sufficient condition that guarantees its existence and uniqueness is stated and proved. The close relationship with Pontryagin's equations is discussed. It is shown that the control problem falls into the framework of optimal linear regulators with quadratic cost functionals. Furthermore, an alternate approach is presented that, for the problem solved, leads to the same optimal control.