Recursive approach to Nash games of quasi-singularly perturbed linear systems

We derive an algorithm for solving the linear-quadratic differential Nash game problem of singularly perturbed systems. It is known that the general steady state solution to the above problem is given in terms of the ill-conditioned coupled algebraic Riccati equations. We show that for a special class, so-called quasi-singularly perturbed systems, the positive definite stabilizing solutions of the coupled Nash algebraic Riccati equations can be obtained in terms of reduced-order well-conditioned algebraic equations corresponding to slow and fast variables