State-space solution to the periodic multirate H∞ control problem: a lifting approach

A two-Riccati equation solution to the H_∞ control problem for periodic multirate systems is derived via the lifting method. The solution is expressed in terms of two algebraic Riccati equations. The causality constraints are represented by a set of positive definiteness conditions and coupling criteria. As a by-product, the study shows that there is a close connection between the solution of the causally constrained lifted problem and the solution obtained by solving the problem directly as a periodic H_∞ problem defined for the multirate system