H 1 Control of Multirate Sampled - Data Systems : A Riccati Equation

A Riccati-equation based state-space solution to the H 1-optimal control problem for periodic multirate sampled-data systems is presented. The solution is characterized by two standard discrete algebraic Ric-cati equations with a set of associated matrix positive deeniteness conditions and coupling criteria. The equations are derived by discretizing a pair of coupled periodic Riccati diierential equations with jumps, which characterize the H 1-optimal controller. An important feature of the proposed solution is the fact that the so-called causality constraint, which is imposed on the controller structure in lifting-based solutions, is automatically satissed. Instead, the solutions to the algebraic Riccati equations are required to satisfy a set of matrix positive deeniteness and coupling conditions, which are easy to check.