Relationships between discrete-time and continuous-time algebraic riccati inequalities

The bilinear transformation is used to establish a direct relationship between a discrete-time algebraic Riccati inequality (DARI) and an associated continuous-time algebraic Riccati inequality (CARI). It is shown that under mild conditions, the DARI is solvable if and only if the corresponding CARI is solvable. The relationship between the DARI and the CARI is then used to translate the general solvability conditions for a CARI given by Scherer into analogous conditions for the DARI. It is shown how such conditions can be applied to determine the solvability of a discrete-time H∞ control problem whose solution set is characterized by two DARIs.