Relationships between discrete-time and continuous-time algebraic Riccati inequalities (Q1377512)

The authors establish a direct relationship between a discrete-time algebraic Riccati inequality (DARI) and an associated continuous-time algebraic Riccati inequality (CARI) by using a bilinear transformation. They show that the DARI is solvable if and only if the corresponding CARI is solvable under mild conditions. Further, they translate the general solvability conditions for a CARI given by Scherer into analogous conditions for the DARI by the use of the relationship between the DARI and the CARI. Lastly, they give an application of these results to the discrete-time \(H_\infty\) control problem.