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 as sociated continuous-time algebraic Riccati inequality (CARI). It is sh own that under mild conditions, the DARI is solvable if and only if th e corresponding CARI is solvable. The relationship between the DARI an d the CARI is then used to translate the general solvability condition s for a CARI given by Scherer into analogous conditions for the DARI. It is shown how such conditions can be applied to determine the solvab ility of a discrete-time H-infinity control problem whose solution set is characterized by two DARIs. (C) 1998 Elsevier Science Inc.