Closed-loop multilevel optimisation of large-scale systems, proposed by Siljak and Sundareshan ( 1977) and Sundareshan (1977), results in the suboptimal performance. This paper determines the closeness of such a suboptimal performance index to the optimal one without computing the optimal solution. It shows that the optimal performance index is bounded between the suboptimal performance index and a lower bound computed from the dual suboptimal system, so that the difference between the suboptimal and optimal performance indices will always be less than the difference between the suboptimal index and the lower bound.
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