The paper presents a new approach for robust control design of multivariable systems via eigenstructure assignment, genetic algorithms and gradient-based optimisation. It takes the combination of the sensitivity and the complementary sensitivity functions of the closed-loop system as the robust control performance index. The gradient calculation of the performance index is described in detail for the closed-loop system with real and complex eigenvalues. The paper makes full use of the freedom provided by eigenstructure assignment to find a controller which stabilises the closed-loop system and minimises the performance index via the combination of genetic algorithms and gradient-based optimisation. The simulation results for the design of a lateral flight control system provide a tutorial demonstration of the power of the method.