In this paper, the soft constrained Nash games for multiparameter singularly perturbed systems (MSPS) are discussed. After establishing the asymptotic structure and local uniqueness of the solution for the cross-coupled sign-indefinite multiparameter algebraic Riccati equations (CSMARE), a new algorithm that is based on Newton's method for solving the CS-MARE is established. As a result, it is shown that the proposed algorithm attains quadratic convergence. Moreover, in order to solve the cross-coupled multiparameter algebraic Lyapunov equation (CMALE) that appears in Newton's method, a new gradient-based iterative algorithm is proposed.
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