On common solutions of Riccati inequalities: for plannar case

Some examples are presented to show the significance of the study of the common positive definite solutions to a set of algebraic Riccati inequalities (ARIs). A necessary and sufficient condition for the existence of common positive definite solutions of a set of second-order Riccati inequalities is derived. This condition provides a new algorithm of computing the common solutions of ARIs. Unlike LMI method, the computing collapse will not occur with the increase of the number of Riccati inequalities due to the fact that our approach handles the ARIs one by one rather than simultaneously.