Local Uniqueness for Nash Solutions of Multiparameter Singularly Perturbed Systems

In this brief, linear quadratic infinite-horizon Nash games for general multiparameter singularly perturbed systems are studied. The local uniqueness and the asymptotic structure of the solutions to the cross-coupled multiparameter algebraic Riccati equation (CMARE) are newly established. Utilizing the asymptotic structure of the solutions to the CMARE, the parameter-independent Nash strategy is established. A numerical example is given to demonstrate the efficiency and feasibility of the proposed analysis