H_∞ control of multirate sampled-data systems: a Riccati equation solution

A Riccati-equation based state-space solution to the H_∞ -optimal control problem for periodic multirate sampled-data systems is presented. The solution is characterized by two standard discrete algebraic Riccati equations with a set of associated matrix positive definiteness conditions and coupling criteria. The equations are derived by discretizing a pair of coupled periodic Riccati differential equations with jumps, which characterize the H_∞ -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 satisfied. Instead, the solutions to the algebraic Riccati equations are required to satisfy a set of matrix positive definiteness and coupling conditions, which are easy to check