Numerical Algorithm for Solving Cross-Coupled Algebraic Riccati Equations of Singularly Perturbed Systems

In this paper, we study the linear quadratic Nash games for infinite horizon singularly perturbed systems (SPS). In order to solve the generalized algebraic Lyapunov equation (GALE) corresponding to the generalized Lyapunov iterations, we propose a new algorithm which is based on the fixed point iterations. Furthermore, we also propose a new algorithm which is based on the Kleinman algorithm for solving the generalized cross-coupled algebraic Riccati equations (GCARE). It is shown that the resulting algorithm guarantees the quadratic convergence.

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