Sampled-data and discrete-time H2 optimal control

H.L. Trentelman, A.A. Stoorvogel

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

6 Citations (Scopus)


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.
Original languageEnglish
Title of host publicationProceedings 32nd IEEE Conference on Decision and Control (San Antonio TX, USA, December 15-17, 1993)
PublisherInstitute of Electrical and Electronics Engineers
Number of pages6
ISBN (Print)0-7803-1298-8
Publication statusPublished - 1993


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