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 mini- mization by linear matrix inequality (LMI) approach. Instead of minimizing the robustly induced L1-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 prob- lem. Based on the result, a sucient 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). Keywords. Uncertain systems, peak-to-peak gain minimization, persistent disturbances, L1-control, non-fragile controllers. AMS (MOS) subject classification: 34K20, 34K35, 34H05, 93D09.