Sampled-data and discrete-time $H_2$ optimal control

H.L. Trentelman, A.A. Stoorvogel

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Abstract

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 we give a treatment of the discrete-time H2 optimal control problem in its full generality. The results we obtain are then applied to the singular discrete-time H2 problem arising from the sampled-data H2 problem. In particular, we give conditions for the existence of optimal sampled data controllers. We also show that the H2 performance of a continuous-time controller can always be recovered asymptotically by choosing the sampling period sufficiently small. Finally, we show that the optimal sampled-data H2 performance converges to the continuous-time optimal H2 performance as the sampling period converges to zero.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages30
Publication statusPublished - 1992

Publication series

NameMemorandum COSOR
Volume9253
ISSN (Print)0926-4493

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