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Maximal Lower Bounds in the Loewner order

Nikolas Stott 1, 2 Xavier Allamigeon 1, 2 Stéphane Gaubert 1, 2 
1 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We show that the set of maximal lower bounds of two symmetric matrices with respect to Loewner order can be identified to the quotient set O(p,q)/(O(p)×O(q)). Here, (p,q)denotes the inertia of the difference of the two matrices, O(p) is the p-th orthogonal group, and O(p,q) is the indefinite orthogonal group arising from a quadratic form with inertia (p,q). We discuss the application of this result to the synthesis of ellipsoidal invariants of hybrid dynamical systems.
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Submitted on : Wednesday, January 27, 2016 - 5:24:18 PM
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  • HAL Id : hal-01263476, version 1


Nikolas Stott, Xavier Allamigeon, Stéphane Gaubert. Maximal Lower Bounds in the Loewner order. 2015 SIAM Conference on Applied Linear Algebra, Oct 2015, Atlanta, United States. ⟨hal-01263476⟩



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