Optimal Guaranteed Cost Control of an Uncertainty System and its Application

The non-fragile guaranteed controller design problem for an interval system and a given cost function is discussed. A sufficient condition is established such that the closed-loop system stability and cost function is guaranteed to be no more than a certain upper bound with all admissible uncertainties as well as a controller gain perturbation uncertainty. A modified interval system described by matrix factorization will lead to less conservative conclusions. An effective linear matrix inequality (LMI) approach is developed to solve the addressed problem. Furthermore, a convex optimization problem is formulated to design the optimal non-fragile guaranteed cost controller which minimizes the upper bound of the closed-loop system cost. The effectiveness of this approach has been verified on a missile launched underwater attitude control system design. Simulation results on a real example are presented to validate the proposed design approach.