离散系统状态反馈下H_2/H_∞同步优化控制问题(英文）

Simultaneous H_2/H_∞ Optimal Control for Discrete-Time Systems:The State Feedback Case

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．

This paper presents a simultaneous H2/Hco optimal control problem for discretetime systems in the state-feedback case. By the use of dynamic state feedback controllers,the design seeks to minimize the H, norm of a closed-loop transfer matrix while simultaneously satisfyinga prescribed H∞ norm bound on some other closed-loop transfer matrix. The class of problems addressed here is relatively general and consists of systems which have left invertible transfer function matrix from the control input to the controlled output. Necessary and sufficient conditions areestablished so that the posed simultaneous H2/Hoo problem is solvable with state feedback controllers.