Worst-case performance measures for linear control problems

Worst-case performance of a controller is defined as the minimum of a quotient of definite integrals. An existence result is given for the worst-case conditions under which the defined performance measure is attained. Also a criterion is given for the evaluation of the performance measure by minimizing a parameter occurring in a boundary value problem. Once the performance measure for a given controller can be evaluated, a nonlinear programming algorithm can be used to choose a controller that maximizes the performance. This problem can be considered as a generalization of the H_∞ optimal control problem over a finite horizon. Considered are convex integrands and time-varying linear systems. Expressions are also given for the variation in performance due to parameter and controller variations. These expressions are useful in evaluating the robustness of the controller