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1620 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL.40, NO. 9, SEPTEMBER 1995 pl(Pate1) pc(Chen)
 

Summary: 1620 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL.40, NO. 9, SEPTEMBER 1995
pl(Pate1) pc(Chen)
0.3820 0.4495
Q + eq.(6)
Lemma I 121: For any two matrices X,Y E Rnxn
At(-YY)= A,(YX).
Lemma 2 [3/: For any two positive definite matrices X, Y E
R" ''
Amin(-rY) L A m i n ( x ) +Amin(lr).
Proposition 1: Let us consider / i c and pk defined in (2) and (4),
respectively. Then one can always find a E > 0 such that
i l k 2/i' (5)
and the trivial one is E = 60 = l/&,(Q-'/'P) > 0.
Pro08
/ / A = X,'!,,K(~FQ- E'PP)
= ~f!,:~ ( ~ l l ~ ( 2 . 1 ~- f r ~ - 1 / a ~ ~ ~ - 1 / 2 ) ~ 1 / r )
= AYl?, (Q(2d,, - F2Q-'/lP"-'"))
= A:!,t,(Q)(2t - E ~ X , , , , ~ ( Q - ~ ' ~ P ~ Q - ' / ~ ) )'/L
2 X~!,~(Q)A,~!~,(2tI,, - C ~ Q - ' / ' P P Q - ' / ~ )
pk(Kim)

  

Source: Aldeen, Mohammad - Department of Electrical and Electronic Engineering, University of Melbourne

 

Collections: Engineering