A new solution for the multivariable minimax optimal robust design problem is presented. The relationship between LQG andH∞design methods is considered and theH∞solution is obtained from the solution of a related LQG problem. The approach provides insights into the relationship between theH∞and LQG design philosophies. The H∞solution involves the same type of steps which are involved in the polynomial–based solutions of the LQG problem, namely spectral factorization and the solution of linear (diophantine) equations. A simplified design procedure is described which requires only the solution of a standard eigenvalue/eigenvector problem.