A controller of interconnected power systems is investigated using an optimal multidimensional variable structure control. The switching hyperplane of the variable structure stabilizer is obtained by minimizing a quadratic performance index in continuous-time. A special feature of the optimal multidimensional variable structure stabilizer is that, when it is operated in the so-called sliding mode, the system response becomes insensitive to changes in the plant parameters. A digital simulation is performed by a digital computer using the Advanced Continuous Simulation Language (ACSL) package, which shows that the dynamic performance of the power system in response to mechanical torque changes is improved when optimal multidimensional variable sturcture stabilizers are employed.