Non-fragile controllers of peak gain minimization for uncertain systems via LMI approach

This paper is concerned with the problem of robust peak-to-peak gain minimization by linear matrix inequality (LMI) approach. Instead of minimizing the robustly induced L_∞-norm, we minimize its upper bound. Results on the state-feedback controllers are obtained by this approach, and the controllers are at most the same order as the plant. One of the main results shows that if there exists a linear dynamic state-feedback controller that achieves a certain level of robust performance, then there exists a static, linear, state-feedback controller that achieves the same performance level, and vice versa. Moreover, the existence of such controllers are equivalent to the existence of solution of an LMI problem. Based on the result, a sufficient condition for obtaining non-fragile state-feedback controller is presented. The condition guarantees simultaneously disturbance rejection in invariant set sense in [2] and the level of performance in [1].