Sampled-Data and Discrete-Time H2 Optimal Control

摘要

The paper deals with the sampled-data H2 optimal control problem. Given a lineartime-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 the paper, the authors give a treatment of the discrete-time H2 optimal control problem in its full generality. The results they obtain 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. The authors also show that the H2 performance of a continuous-time controller can always be recovered asymptotically by choosing the sampling period sufficiently small. Finally, the authors show that the optimal sampled-data H2 performance converges to the continuous-time optimal H2 performance as the sampling period converges to zero.