The H/sub 2/ guaranteed cost control problem for a singularly perturbed norm-bounded uncertain system is addressed using the quadratic stabilizability framework. After defining the corresponding slow and fast uncertain subsystems, the set of quadratic stabilizing composite controls is characterized. Two Riccati equations have to be solved, one for the slow subsystem and the other for the fast subsystem. Choosing appropriately the weighting matrices, it is shown how to pick up in the set of quadratic stabilizing composite controls, a control minimizing an upper bound on the H/sub 2/ norm of a certain transfer matrix. The case of the guaranteed cost control problem for the reduced system is also investigated.
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机译:使用二次稳定性框架解决了奇摄动范数有界不确定系统的H / sub 2 /保证成本控制问题。在定义了相应的慢速和快速不确定子系统之后,对二次稳定复合控制集进行特征化。必须求解两个Riccati方程,一个方程用于慢子系统,另一个方程用于快速子系统。适当选择权重矩阵,显示了如何在一组二次稳定复合控件中选取该控件,该控件使某个传递矩阵的H / sub 2 /范数的上限最小。还研究了简化系统的保证成本控制问题的情况。
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