Now consider one method of selecting feedback gains which will make

the linearized system behave as though it were time-invariant.      First

make the definition


(6-16)


where K1,1(t) corresponds to feedback of the joint positions and K1,2(t) corresponds to feedback of the joint velocities.    Using (6-11) through (6-13) it is possible to write the linearized system matrix as


F*(t) -G

  L -BH


(6-17)


         INxN

F2(t) - d-l1 (6**)Ki,2(t)

         0


    0

-JO )K2(t)

    A


     We desire a feedback law which will make the right-hand side of (6-17) take the following form


0
   Mi
   -B


INx
M2
0


(6-18)


where M, c RNxN, M2 E RNxN, and M3 e RNxrN are constant matrices (note that A e RrNxrN). It can be shown that the eigenvalues of (6-18) can be assigned arbitrarily by proper choice of M1, M2 and M3.     This is, in


          0
Fl1(t) - J-l( *)Kl1,l(t)

         -B


Klmt := [Kl,l(t), K1,2(t)]