Linear Quadratic differential games and their Open-Loop Nash Equilibrium (OL-NE) strategies are studied with a threefold
objective. First, it is shown that the state/costate lifted system (arising from the application of Pontryagin’s Minimum Principle)
is such that its behavior restricted to the equilibrium subspace can be interpreted as the (non-power-preserving) interconnection
of two cyclo-passive Port-Controlled Hamiltonian systems. Such PCH systems constitute the best response generators for each
player, thus mimicking and extending the corresponding interpretation of (single-player) optimal control problems. Second, by
realizing that the behavior of the lifted dynamics off the equilibrium subspace is “irrelevant” for generating the equilibrium
strategies, it is shown that such an invariant subspace can be rendered, via a suitably constructed virtual input, externally
asymptotically stable while preserving the OL-NE. Finally, based on these premises we provide a closed-form gradient-descent
method to solve the asymmetric coupled Riccati equations characterising the OL-NE strategies.