H∞ control of multirate sampled-data systems:: A state-space approach

A state-space solution of the H-infinity control problem for periodic multirate sampled-data systems is presented. The solution is characterized in terms of a pair of discrete algebraic Riccati equations with a set of associated matrix positive-definiteness conditions and coupling criteria. The solution is derived using two different approaches. In the first approach, the solution is obtained by discretizing two coupled periodic Riccati equations with jumps which characterize the H-infinity-optimal controller. The second approach is based on the lifting technique. The H-infinity-optimal controller for a lifted representation of the multirate system is characterized by a two-Riccati equation solution, in which the so-called causality constraint is represented by a set of positive-definiteness conditions and coupling criteria. (C) 1998 Elsevier Science Ltd. All rights reserved.