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Transient energy growth suppression is a common control objective forfeedback flow control aimed at delaying transition to turbulence. A prevailingcontrol approach in this context is observer-based feedback, in which afull-state feedback controller is applied to state estimates from an observer.The present study identifies a fundamental performance limitation ofobserver-based feedback control: whenever the uncontrolled system exhibitstransient energy growth in response to optimal disturbances, control byobserver-based feedback will necessarily lead to transient energy growth inresponse to optimal disturbances for the closed-loop system as well. Indeed,this result establishes that observer-based feedback can be a poor candidatefor controller synthesis in the context of transient energy growth suppressionand transition delay: the performance objective of transient energy growthsuppression can never be achieved by means of observer-based feedback. Further,an illustrative example is used to show that alternative forms of outputfeedback are not necessarily subject to these same performance limitations, andshould also be considered in the context of transient energy growth suppressionand transition control.

Performance limitations of observer-based feedback for transient energy growth suppression