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Papageorgiou, “Robust H-infinity Loop Shaping and Aerospace Applications,” PhD Thesis, July 1998. [14] G. V. Murphy and J. M. Bailey, “Robust Control Technique for Nuclear Power Plants,” Instrumentation and Controls Division, Oak Ridge National Laboratory, ORNL/TM-10916, March 1989. [15] H. Kwakernaak and R. Sivan, “Linear Optimal Control Systems,” Wiley-Interscience, New York, 1972. ,”Springer-Verlag, Berlin, 1995. , “Passive adaptive control of nonlinear systems,” International Journal of Adaptive Control and Signal Processing, vol.

The constant state weighting matrix Q0 is selected to be symmetric and at least positive semi-definite and the control weighting matrix R1 is selected to be symmetric and positive definite. Under these assumptions the value of J1 is nonnegative. The optimal control vector upq(t) is generated from the state perturbation xpq(t) by a linear constant gain feedback upq(t) = -Kxpq(t) (13) where K is a constant feedback gain matrix given by K = R1 −1 B pq T P1 (14) and P 1 is a constant symmetric positive definite matrix which is the solution of the algebraic matrix Riccati equation, P1 A pq − AT pq P1 − Q1 + P1 B pq R1−1 B T pq P1 = 0 (15) Then we can show that u pq = − Kx pq (t ) = − K1 x p − K 2 q where K = [K 1 K2 ] (16) The existence and uniqueness of solution for the above equation are guaranteed by the following assumptions: 1.

21] Mayergoyz, I. , “Mathematical Models of Hysteresis,” Springer-Verlag, Berlin, 1991. [22] Merritt, H. , New York, 1967. A. V. Kokotovic, “ Robust Nonlinear Control Design,” SpringerVerlag, 1996 [25] R. J. : Princeton University Press, 1961. , P. V. , Rhode and J. Winkelman, “Adaptive nonlinear control of systems containing a dead-zone,” Proc. of the 30th IEEE Conference on Decision and Control, pp. 2111-2115, Brighton, England, 1991. [27] Robust Control Techniques, Tutorial Document, Group for Aeronautical Research and Technology in EURope (GARTEUR), April 4, 1997.

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