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本文提出一个离散系统状态反馈下HZ／H∞同步优化控制问题．本文提出的问题是利用设计动态状态反馈控制器来使某闭环传递函数的H2范数达到最优，同时也使另一闭环传递函数满足预先给定的H∞范数值．本文所考虑的系统有相当之普遍性，只要求其中一个从控制输人到被控制输出的开环传递函数是左可逆．本文也建立了所提出的HZ／H∞同步优化控制问题有解之充分和必要条件．
In this paper, we propose a HZ / H∞ synchronization optimization control problem with discrete system state feedback. The problem posed in this paper is to design the dynamic state feedback controller to optimize the H2 norm of a closed loop transfer function and to make the other closed loop transfer function satisfy a given H∞ norm. The system considered in this paper is quite general. It is only required that one of the open-loop transfer functions from the control input to the controlled output be left-invertible. This paper also establishes the sufficient and necessary conditions for the proposed HZ / H∞ synchronization optimization control problem.