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本文给出奇异摄动系统Ｈ∞问题有解的一个简洁的ε－独立充要条件，并给出Ｈ∞控制器的具体形式．同时本文证明该控制器亦具有奇异摄动性，并且其快、慢部分分别为原系统的快、慢子系统之Ｈ∞问题的次优控制器．本文结果亦适用于非标准摄动情形．
In this paper, we give a concise ε-independent sufficient and necessary condition for solving the H∞ problem of singularly perturbed systems and give the concrete form of H∞controller. At the same time, this paper proves that the controller also has singular perturbation, and its fast and slow parts are suboptimal controllers for the H∞ problems of the fast and slow subsystems of the original system. The results of this paper also apply to non-standard perturbation situation.