ABSTRACT
The essential feature of the proposed method is the conversion of the system (2.1) to the block control (BC) form consisting of r blocks:
x˙1 = f1(x1, t)+B1(x1, t)x2+g1(x1, t),
x˙i = fi(x¯i, t)+Bi(x¯i, t)xi+1+gi(x¯i, t), (2.3) x˙r = fr(x¯r, t)+Br(x¯r, t)u+gr(x¯r, t),
where the vector x is decomposed as x = (x1,x2, . . . ,xr,xr+1)T , x¯i = (x1, . . . ,xi)T , i = 2, . . . ,r, xi is a n j× 1 vector, and the indices (n1,n2, . . . ,nr) define the structure of the system and satisfy the following relation:
n1 ≤ n2 ≤ ·· · ≤ nr ≤ m and r
ni = n. (2.4)
The matrix Bi, multiplying the fictitious xk+1 in each ith block of (2.3), has full rank, that is,
n . . .
