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

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Problem 1.11

Riccati stability

Erik I. Verriest1

School of Electrical and Computer Engineering

Georgia Institute of Technology

Atlanta, GA, 30332-0250

USA

erik.verriest@ee.gatech.edu

1 DESCRIPTION OF THE PROBLEM

Given two n×n real matrices, A and B, consider the matrix Riccati equation

-1743749119

Can one characterize the pairs (A, B) for which the above equation has a solution for positive definite symmetric matrices P, Q, and R?

In [8] a pair (A, B) was defined to be Riccati stable if a triple of positive definite matrices P, Q, R exists such that (1) holds.

The problem may be stated equivalently as an LMI:

Can one characterize all pairs (A, B) without ...

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