Computation of the Stabilizing Solution of Nash-Riccati Equations

Consider an iterative modification of the linearized Newton method for computing the minimal nonnegative solution of a a nonsymmetric Nash-Riccati equation. The equation has arisen in linear quadratic games for positive systems. The Newton procedure for computing the minimal nonnegative solution is well known in the the literature. Our proposal is effective one because it employs small number of matrix multiplication at each iteration step and there is a variant to exploit the block structure of matrix coefficients of the Nash-Riccati equation. Moreover, in this reason, it is easy to extend the proposed iterative modification depending on the number of players of a given game model. We provide a numerical example where compare the results from experiment with the proposed iteration an the linearized Newton method.