The Nash Equilibrium Point in the LQ Game on Positive Systems with Two Players

Abstract: We consider the linear quadratic differential games for positive linear systems with the feedback information structure and two players. The Newton method to obtain the stabilizing solution of a corresponding set of Riccati equations is presented in the literature. Here, we modify the Newton method and propose a new faster iterative method. Moreover, the convergence properties of the modification are investigated and the sufficient condition to apply the modification is derived. The performances of the proposed algorithm are illustrated on some numerical examples.