This paper deals with the sampled-data H/sub 2/ optimal control problem. Given a linear time-invariant continuous-time system, the problem of minimizing the H/sub 2/ performance over all sampled-data controllers with a fixed sampling period can be reduced to a pure discrete-time H/sub 2/ optimal control problem. This discrete-time H/sub 2/ problem is always singular. Motivated by this, in this paper the authors give a treatment of the discrete-time H/sub 2/ optimal control problem in its full generality. The results obtained are then applied to the singular discrete-time H/sub 2/ problem arising from the sampled-data H/sub 2/ problem. In particular, the authors give conditions for the existence of optimal sampled data controllers. It is also shown that the H/sub 2/ 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 H/sub 2/ performance converges to the continuous time optimal H/sub 2/ performance as the sampling period converges to zero.
|Title of host publication||Proceedings 32nd IEEE Conference on Decision and Control (San Antonio TX, USA, December 15-17, 1993)|
|Publisher||Institute of Electrical and Electronics Engineers|
|Number of pages||6|
|Publication status||Published - 1993|