Title :
H∞ and H2 optimal controllers for periodic and multi-rate systems
Author :
Voulgaris, Petros G. ; Dahleh, Munther A. ; Valavani, Lena S.
Author_Institution :
Lab. of Inf. & Decision Syst., MIT, Cambridge, MA, USA
Abstract :
The solutions to the optimal l2 to l 2 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
Keywords :
discrete time systems; optimal control; sampled data systems; H∞ control; H2 control; Hilbert spaces; LQG; Nehari´s theorem; causality condition; l2 disturbance rejection problem; linear quadratic Gaussian; linear time invariant compensator; multirate sampled data systems; optimal control; periodic systems; projection theorem; Closed loop systems; Control systems; Ear; Gaussian noise; H infinity control; Hilbert space; Optimal control; Sampled data systems; Time measurement; Time varying systems; White noise;
Conference_Titel :
Decision and Control, 1991., Proceedings of the 30th IEEE Conference on
Conference_Location :
Brighton
Print_ISBN :
0-7803-0450-0
DOI :
10.1109/CDC.1991.261291
