The Sampled-data H 1 Problem: a Uniied Framework for Discretization Based Methods and Riccati Equation Solution

A new discretization based solution to the sampled-data H 1 control problem is given. In contrast to previous solution procedures, the method is not based on the lifting technique. Instead, an equivalent nite-dimensional discrete problem representation is derived directly from a description of the sampled-data system. This is achieved via a closed-loop expression of the worst-case intersample disturbance and an associated variable transformation. In this way the solution is obtained completely in terms of classical linear-quadratic optimal control theory. The discretization procedure described here is closely related to both the lifting-based technique and a two-Riccati equation solution of the sampled-data H 1 problem, in which the solution is obtained in terms of two coupled Riccati diierential equations with jumps. In this way the method makes the connections between the various solution procedures transparent. In particular , it can be shown that the lifting approach and the two-Riccati equation solution lead to identical synthesis equations for the H 1-optimal sampled-data controller.