Sampled-data and discrete-time H2 optimal control

This paper deals with the sampled-data H₂ optimal control problem. Given a linear time-invariant continuous-time system, the problem of minimizing the H₂ performance over all sampled-data controllers with a fixed sampling period can be reduced to a pure discrete-time H₂ optimal control problem. This discrete-time H₂ problem is always singular. Motivated by this, in this paper the authors give a treatment of the discrete-time H ₂ optimal control problem in its full generality. The results obtained are then applied to the singular discrete-time H₂ problem arising from the sampled-data H₂ problem. In particular, the authors give conditions for the existence of optimal sampled data controllers. It is also shown that the H₂ performance of a continuous-time controller can always be recovered asymptotically by choosing the sampling period sufficiently small. Finally, it is shown that the optimal sampled-data H₂ performance converges to the continuous time optimal H₂ performance as the sampling period converges to zero