Insensitive dynamic output feedback control with mixed-H∞ norm sensitivity minimization

This paper will focus on designing insensitive output feedback controllers for linear continuous-time systems with mixed-H∞ norm sensitivity minimization. In order to reduce the sensitivity of the designed controllers, a type of coefficient sensitivity function with respect to additive controller coefficient variations is defined. What's more, the H∞ norms of the coefficient sensitivity functions are regarded as sensitivity indexes. Then, the considered problem in this paper is reduced to a multi-objective problem which is to be a non-convex optimization problem, where both the coefficient sensitivity constraint and the standard H∞ norm constraint are considered simultaneously. To solve this non-convex problem, a two-step procedure is adopted to obtain the solutions through satisfying a set of linear matrix inequalities (LMIs). It is worth to mention here that the non-fragile control method is adopted to obtain an effective initial solution of the two-step procedure. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed design procedure.