Abstract
In this paper we study the linear quadratic Nash Game strategies for a singularly perturbed systems. In order to obtain the optimal closed loop strategies, we must solve the cross-coupled generalized algebraic Riccati equations with small parameter ε. The main results in this paper is to propose a new recursive algorithm by making use of a Lyapunov iterations. Using a Lyapunov iterations and the recursive algorithm, we show that the solution of the cross-coupled generalized algebraic Riccati equations converges to a positive semi-definite solutions with the rate of convergence of O(εk+1) where k is a iteration number of recursive algorithm. Furthermore, in order to show the effectiveness of the proposed algorithms, numerical examples are included.
