  Converse optimality theory addresses an optimal control problem conversely
where the system is unknown and the value function is chosen. Previous work
treated this problem both in continuous and discrete time and non-extensively
considered disturbances. In this paper, the converse optimality theory is
extended to the class of affine systems with disturbances in continuous time
while considering norm constraints on both control inputs and disturbances. The
admissibility theorem and the design of the internal dynamics model are
generalized in this context. A robust stabilizability condition is added for
the initial converse optimality probelm using inverse optimality tool: the
robust control Lyapunov function. A design for nonlinear class of systems that
are both robustly stabilizable and globally asymptotically stable in open loop
is obtained. A case study illustrates the presented theory.
