On algebraic Riccati equations associated with M -matrices
نویسنده
چکیده
We consider the algebraic Riccati equation for which the four coefficient matrices form an M -matrix K. When K is a nonsingular M -matrix or an irreducible singular M -matrix, the Riccati equation is known to have a minimal nonnegative solution and several efficient methods are available to find this solution. In this paper we are mainly interested in the case where K is a reducible singular M -matrix. Under a regularity assumption on the M -matrix K, we show that the Riccati equation still has a minimal nonnegative solution. We also study the properties of this particular solution and explain how the solution can be found by existing methods.
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