THE DETERMINATION OF FEEDBACK GAINS FOR UNCERTAIN LINEAR-SYSTEMS USING HIGHER-ORDER SENSITIVITY MINIMIZATION

To reduce the influence of large parameter variation on the response o f linear systems, this paper considers the design of controllers that minimize the higher-order sensitivities. Here the higher-order sensiti vities are defined as the second-order, third-order, etc. partial deri vatives of the state and control vectors with respect to the uncertain parameter. The feedback gains are obtained by minimizing a quadratic cost function that includes state and control sensitivities of arbitra ry order. The paper also presents an efficient numerical procedure for solving the resultant system of non-linear matrix equations. The effe ctiveness of the approach is demonstrated by the design of an output f eedback controller for an electromagnetic suspension. By comparison wi th standard design approaches it is shown that higher-order sensitivit y minimization can be used to reduce the deviation from the nominal tr ajectory caused by parameter variation.