On the bilinear transformation of Riccati equations

An interpretation of the bilinear transformation of the Riccati equation is presented. The bilinear transformation of a continuous type algebraic Riccati equation (ARE) to a discrete type ARE, and its inverse transformation, have been used for solving ARE numerically. However, its physical meaning has not been clear, and the problem formulation was complicated. This note gives a physical interpretation and derivation of the bilinear transformation of the ARE. Finally, cheap control for continuous-time linear systems is considered from the view of the bilinearly transformed system.