Minimax design of optimal stochastic multivariable systems

A new minimax optimal control problem is considered for a stochastic multivariable system. The cost function involves the trace of a weighted sum of spectral density matrices whose frequency response is to be limited. The H_infinity -norm of this scalar function is therefore minimised. To obtain the solution of the minimax control problem, an auxiliary lemma is employed. This enables an equivalent LQG optimal problem to be constructed which has the desired controller as its solution. An advantage of the particular cost function employed is that the solution is obtained more easily than for the general multivariable H_infinity problem. This makes the approach easier to understand and the results simpler.