Nonsymmetric algebraic Riccati theory: A matrix pencil approach

A nonsymmetric continuous-time algebraic Riccati system which incorporates as particular cases various nonsymmetric algebraic Riccati equations is studied under assumptions on the matrix coefficients utterly relaxed. Necessary and sufficient existence conditions together with a numerical algorithm for the stabilizing solution to the algebraic Riccati system are given. 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.