Asymptotic Expansions of Solutions of Cross–Coupled Algebraic Riccati Equations of Multimodeling Systems Related to Nash Games

Abstract — The linear quadratic Nash games for infi-nite horizon multiparameter singularly perturbed sys-tems (MSPS) are considered. The existence of bounded solutions and asymptotic expansions of solutions for the generalized cross–coupled multiparameter algebraic Riccati equations (GCMARE) are established without non–singularity assumptions of the fast subsystems. I