TY - GEN

T1 - H∞ and H2 optimal controllers for periodic and multi-rate systems

AU - Voulgaris, Petros G.

AU - Dahleh, Munther A.

AU - Valavani, Lena S.

N1 - Funding Information:
Acknowledgements--The first and third authors were supported by the AFOSR-Elgin A.F.B. under grant F08635-87-K-0031, by the NASA Ames and Langley Research Centers under grant NASA/NAG-2-297 and by a gift from the Boeing Corporation. The second author was supported by the Draper Laboratory grant DC-H-441636 and by NSF grant 9157306-ECS.

PY - 1992/1

Y1 - 1992/1

N2 - The solutions to the optimal l2 to l2 disturbance rejection problem (H∞) as well as to the LQG (linear quadratic Gaussian) (H2) problem in periodic systems using the lifting technique are presented. Both problems involve a causality condition on the optimal LTI (linear time invariant) compensator when viewed in the lifted domain. The H∞ problem is solved using the Nehari's theorem, whereas in the H2 problem the solution is obtained using the projection theorem in Hilbert spaces. The authors demonstrate that exactly the same method of solution to the H∞ and H2 problems in periodic systems applies when considering the same problems in multirate sampled data systems.

AB - The solutions to the optimal l2 to l2 disturbance rejection problem (H∞) as well as to the LQG (linear quadratic Gaussian) (H2) problem in periodic systems using the lifting technique are presented. Both problems involve a causality condition on the optimal LTI (linear time invariant) compensator when viewed in the lifted domain. The H∞ problem is solved using the Nehari's theorem, whereas in the H2 problem the solution is obtained using the projection theorem in Hilbert spaces. The authors demonstrate that exactly the same method of solution to the H∞ and H2 problems in periodic systems applies when considering the same problems in multirate sampled data systems.

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M3 - Conference contribution

AN - SCOPUS:0026618424

SN - 0780304500

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 214

EP - 216

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Publ by IEEE

T2 - Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3)

Y2 - 11 December 1991 through 13 December 1991

ER -