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Finite-dimensional compensators for the H-optimal control of infinite-dimensional system via a Galerkin-type approximation

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2 Author(s)
MingQing Xiao ; Dept. of Math., California Univ., Davis, CA, USA ; T. Basar

We study the existence of general finite-dimensional compensators in connection with the H-optimal control of linear time-invariant systems on a Hilbert space with noisy output feedback. The approach adopted uses a Galerkin-type approximation, where there is no requirement for the system operator to have a complete set of eigenvectors. We show that if there exists an infinite-dimensional compensator delivering a specific level of attenuation, then a finite-dimensional compensator exists and achieves the same level of disturbance attenuation. In this connection, we provide a complete analysis of the approximation of infinite-dimensional generalized Riccati equations by a sequence of finite-dimensional Riccati equations. As an illustration of the theory developed, we provide a general procedure for constructing finite-dimensional compensators for robust control of flexible structures

Published in:

Decision and Control, 1999. Proceedings of the 38th IEEE Conference on  (Volume:2 )

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