  We studied structural and magnetic properties of a series of insulating
double perovskite compounds, La$_{2-x}$Sr$_{x}$CuRuO$_{6}$ (0 $\le$ x $\le$ 1),
representing doping via \textit{A}-site substitution. The end members
La$_{2}$CuRuO$_{6}$ and LaSrCuRuO$_{6}$ form in monoclinic structure while the
intermediate Sr doped compounds stabilise in triclinic structure. The Cu and Ru
ions sit on alternate B-sites of the perovskite lattice with $\sim$15%
anti-site defects in the undoped sample while the Sr doped samples show a
tendency to higher ordering at B-sites. The undoped (x = 0) compound shows a
ferrimagnetic-like behaviour at low temperatures. In surprising contrast to the
usual expectation of an enhancement of ferromagnetic interaction on doping, an
antiferromagnetic-like ground state is realized for all doped samples (x $>$
0). Heat capacity measurements indicate the absence of any long range magnetic
order in any of these compounds. The magnetic relaxation and memory effects
observed in all compounds suggest glassy dynamical properties associated with
magnetic disorder and frustration. We show that the observed magnetic
properties are dominated by the competition between the nearest neighbour Ru --
O -- Cu 180$^\circ$ superexchange interaction and the next nearest neighbour Ru
-- O -- O -- Ru 90$^\circ$ superexchange interaction as well as by the
formation of anti-site defects with interchanged Cu and Ru positions. Our
calculated exchange interaction parameters from first principles calculations
for $x$ = 0 and $x$ = 1 support this interpretation.
