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The Shapley Folkman lemma was introduced as a step in the proof of the Shapley Folkman theorem, which states an upper bound on the distance between the Minkowski sum and its convex hull.
Starr's corollary states an upper bound on the Euclidean distance between the Minkowski sum of N sets and the convex hull of the Minkowski sum; this distance between the sum and its convex hull is a measurement of the non-convexity of the set.
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With resort to state augmentation and Riccati difference equations, an upper bound on the filtering error covariance is obtained for all admissible uncertainties.
Kreher and Rees (Codes an Designs, Ohio state University Research Institute Publication, 10 (2002) 179) derived an upper bound on the size of the hole, which is given here in Theorem 3.
"While it's safe to say that Missouri is likely a center-right state now," Mr. Calfano said, "the Akin controversy might be an indicator of an upper bound on how much the state electorate will tolerate right-wing rhetoric".
This implies an upper bound on the required state space size that holds uniformly for all RL problems.
Instead, one only knows an upper bound on the delays, and we allow the upper bound to be arbitrarily large.
This extension gives an upper bound on the number of state changes along the edges of the network.
The resulting fuzzy observer can exponentially stabilize the augmented system while providing an upper bound on the cost function of state estimation error.
Mao (2013) also obtains an upper bound on the duration τ between two consecutive state observations.
The latter problem can be addressed partially by using the CFTP under the approximation that there is an upper bound on the number of molecules in the state space.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com