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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 10.1

Root-clustering for multivariate

polynomials and robust stability analysis

Pierre-Alexandre Bliman

INRIA

Rocquencourt BP 105

78153 Le Chesnay cedex

France

pierre-alexandre.bliman@inria.fr

1 DESCRIPTION OF THE PROBLEM

17515

17517

Problem (2, 3) is a linear matrix inequality in the m + 1 unknown matrices P, Q1, . . . , Qm, a convex optimization problem.

The LMIs (2, 3) obtained for increasing values of k constitute indeed a family of weaker and weaker sufficient conditions for (1). Conversely, property (1) necessarily implies solvability of the ...

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