The objective of this paper is to introduce the essential ingredients of linear systems and control theory to the fluid mechanics community, to discuss the relevance of this theory to important open problems in the optimization, control, and forecasting of practical flow systems of engineering interest, and to outline some of the key ideas that have been put forward to make this connection tractable. Although many significant advances have already been made, many new challenges lie ahead before the full potential of this synthesis of disciplines can be realized.
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