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The coupled system evolves according to: [ \begincases \dotx_L = A_L x_L + B_L \Phi^-1(x_M) + \eta_L \ \dotx_M = A_M x_M + B_M \Phi(x_L) + \eta_M \endcases ] where (\eta) denotes noise terms. The paper proves (Stability of the Coupled System) using Lyapunov functions, establishing that if the eigenvalues of (A_L) and (A_M) lie in the left half‑plane and (|\Phi|_2 < \gamma), the joint system is asymptotically stable. The coupled system evolves according to: [ \begincases