sum(norms(Z,p,2)) does what you want.
norms Computation of multiple vector norms.
norms( X ) provides a means to compute the norms of multiple vectors
packed into a matrix or N-D array. This is useful for performing
max-of-norms or sum-of-norms calculations.
All of the vector norms, including the false "-inf" norm, supported
by NORM() have been implemented in the norms() command.
norms(X,P) = sum(abs(X).^P).^(1/P)
norms(X) = norms(X,2).
norms(X,inf) = max(abs(X)).
norms(X,-inf) = min(abs(X)).
If X is a vector, these computations are completely identical to
their NORM equivalents. If X is a matrix, a row vector is returned
of the norms of each column of X. If X is an N-D matrix, the norms
are computed along the first non-singleton dimension.
norms( X, , DIM ) or norms( X, 2, DIM ) computes Euclidean norms
along the dimension DIM. norms( X, P, DIM ) computes its norms
along the dimension DIM.
Disciplined convex programming information:
norms is convex, except when P<1, so an error will result if these
non-convex "norms" are used within CVX expressions. norms is
nonmonotonic, so its input must be affine.