*Problem 1.11*

Riccati stability

Erik I. Verriest^{1}

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

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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