本文主要探討穩定非線性非時變輸入仿射系統之平衡化處理。吾人首先利用對局理論以及參數最佳化技巧計算此類系統之Hankel 範數，並基於Lagrange 乘數之連續性建構其計算方法，以取代求解一組偏微分方程之作法。最後，吾人推導此系統之平衡化實現之演算法則步驟。文中舉例說明Hankel 範數之計算過程及平衡化之作法。

In this paper, we are concerned with the balancing for stable nonlinear time invariant input-affine system.Firstly, the system’s Hankel norm is computed via game theoretical approach incorporating with the
parameter optimization technique. This computation algorithm is derived based on the continuity of the costate vector at present time, which leads to a benefit to avoid solving the controllability and observability
functions through a set of partial differential equations. Afterward, the balanced realization is conducted.Certain numerical examples are used to demonstrate the computational technique for Hankel norm and
balanced realization.