Near–Optimal Nash Strategy for Multiparameter Singularly Perturbed Systems

Abstract—In this paper, the linear quadratic Nash games for infinite horizon multiparameter singularly perturbed systems (MSPS) are discussed. The uniqueness and the asymptotic structure of the solution to the generalized cross–coupled multiparameter algebraic Riccati equations (GCMARE) are newly established without the nonsingularity assumptions for the fast state matrices. The main contribution of this paper is that a construction of high–order approximations to a strategy that guarantees a desired performance level on the basis of a new iterative technique is proposed. As a result, it is shown that the high–order accuracy strategy improves the performance. I