Sampled-Data and Discrete-Time H2 Optimal Control

摘要

The sampled data H(sub 2) optimal control problem is addressed. 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, a treatment of the discrete time H(sub 2) optimal control problem in its full generality is given. The results obtained are applied to the singular discrete time H(sub 2) problem arising from the sampled data H(sub 2) problem. In particular, conditions for the existence of optimal sampled data controllers are given. The H(sub 2) performance of a continuous time controller can always be recovered asymptotically by choosing the sampling period sufficiently small. 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.