Solving the coupled Riccati equation for the N-players LQ differential game

A solution for the Differential Riccati Equation arises from the N-Players LQ differential game is presented. The game solution corresponds to a Nash-equilibrium point of this game. The approach is based on extending the state vector that allows to present the classical result (N Coupled Riccati Equations) as a single Extended Coupled Riccati Differential Equation that can be solved by standard methods. Thus the Nash equilibrium is found in an easier way. The effectiveness of the designed strategy is illustrated by two examples.