Non-symmetric algebraic Riccati theory: A matrix pencil approach
Résumé
A non–symmetric continuous–time algebraic Riccati system which incorporates as particular cases various non–symmetric algebraic Riccati equations is studied under assumptions on the matrix coefficients relaxed as far as possible. Necessary and sufficient existence conditions together with computable formulas for the stabilizing solution are given in terms of proper deflating subspaces of an associated matrix pencil. A numerical algorithm able to decide existence and to compute the stabilizing solutions, if any, to the algebraic Riccati system is proposed. The results may be applied in the framework of game theory to design Nash and Stackelberg strategies without the classical invertibility assumption on the direct feed–through matrix coefficient.