  We consider optimization of linear stability of synchronized states between a
pair of weakly coupled limit-cycle oscillators with cross coupling, where
different components of state variables of the oscillators are allowed to
interact. On the basis of the phase reduction theory, the coupling matrix
between different components of the oscillator states that maximizes the linear
stability of the synchronized state under given constraints on overall coupling
intensity and on stationary phase difference is derived. The improvement in the
linear stability is illustrated by using several types of limit-cycle
oscillators as examples.
