Optimal H ∞ multivariable robust controllers and the relationship to LQG design problems

Abstract

A new solution for the multivariable minimax optimal robust design problem is presented. The relationship between LQG and H ∞ design methods is considered and the H ∞ solution is obtained from the solution of a related LQG problem. The approach provides insights into the relationship between the H ∞ 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.