LMI based minimax control under component-wise constraints on the inputs with application to an electric power steering system

The minimax control problem is considered for the linear MIMO system acted on by a stochastic input. The input can include disturbances, sensor noise and reference signals. The performance index is the maximum of the system output variance over the class of inputs, which is specified by the component-wise integral restrictions on the input spectral measure. The problem is to minimize the performance index over the class of stabilizing controllers. It is shown that the problem can be reduced to the minimization of the linear functional over the solutions set of the system of linear matrix inequalities (LMIs). The system of inequalities has the structure reminiscent of the LMI that are used in H^∞ optimization. The result obtained is applied to the controller synthesis for an electric power assist steering system