New Expressions of 2 , ˟, 2 Block Matrix Inversion and Their Application

where ~ Q 2 3n is the column vector composed of all the vectors ~ qj, for j = 1;. .. ;n, and the matrix M(t) = [m jk (t)] 2 n2n is given by; m jj (t) = 1j + n k=1 k p jk ~ k , and m jk (t) = 0k p jk ~ j. We can see that the formation has converged to the desired trajectory and consequently all spacecraft are aligned only if ~ Q = 0. A necessary and sufficient condition for this is that the matrix M(t) has full rank. We can easily verify that matrix M(t) is strictly diagonally dominant if condition (21) is satisfied, [1]. This implies that the only solution of (A6) is ~