Continuous-Time Non-Symmetric Algebraic Riccati Theory: A Matrix Pencil Approach

A continuous–time non–symmetric algebraic Riccati system which incorporates as a particular case the non– symmetric algebraic Riccati equation 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 numerically–sound algorithm able to decide existence and to compute the stabilizing solutions, if any, to the algebraic Riccati system is recalled. The whole development may be applied to fluid queues, transport theory, and game theory with an open–loop information structure without assuming the classical invertibility hypothesis on the quadratic matrix coefficient.