On the structure of H2-optimal sampled-data controllers

This paper is concerned with the H₂ problem of sampled-data systems with their intersample behavior taken into account. It is well known that the problem reduces to an equivalent discrete-time H₂ problem, which is always singular. In this paper, we show that if the generalized plant of the original problem satisfies the standard assumptions usually made in the continuous-time H₂ and H_∞ problems, then the reduced problem can actually be solved without any essential difficulties. Namely, the singularity can be circumvented by solving a reduced-order Riccati equation, and the Kalman filter associated with the optimal controller reduces to a minimal-order observer