I was inspired to copy the recently (as of 2.077) added dupN to make inflateN, which does the converse of dupN, suitable for Kronecker products.

sub PDL::inflateN {
  my ($this, @times) = @_;
  return $this->copy if !grep $_ != 1, @times;
  my $sl = join ',', map "*$_,:", @times;
  $this = $this->slice($sl);
  $this = $this->clump($_, $_+1) for 0..$#times;
  $this;
}

pdl> p $a = pdl '[[1 2][3 4]]'
[
 [1 2]
 [3 4]
]
pdl> p $b = pdl '[[5 6][7 8][9 10]]'
[
 [ 5  6]
 [ 7  8]
 [ 9 10]
]
pdl> p $a->inflateN($b->dims)
[
 [1 1 2 2]
 [1 1 2 2]
 [1 1 2 2]
 [3 3 4 4]
 [3 3 4 4]
 [3 3 4 4]
]
pdl> p $b->dupN($a->dims)
[
 [ 5  6  5  6]
 [ 7  8  7  8]
 [ 9 10  9 10]
 [ 5  6  5  6]
 [ 7  8  7  8]
 [ 9 10  9 10]
]
sub kron { my ($x,$y) = @_; $x->inflateN($y->dims) * $y->dupN($x->dims
+) }
pdl> p kron($a,$b)
[
 [ 5  6 10 12]
 [ 7  8 14 16]
 [ 9 10 18 20]
 [15 18 20 24]
 [21 24 28 32]
 [27 30 36 40]
]
[download]

The above will broadcast nicely over any number of dimensions, not just 2. inflateN has been added and will be in the next PDL release (2.081).