Stability analysis and performance improvement of uncertain linear systems with designing of a suitable reset law

In reset control systems, the reset law is a main characteristic of the reset controllers. In this study, a model prediction-based framework is proposed to determine a suitable reset law for the uncertain linear control system. For achieving this goal, first a typical uncertain linear plant is considered and then the state space of the closed-loop system, which consists of the uncertain plant and a linear controller, is formulated. The stability problem of such uncertain system is translated into a feasibility assessment of some linear matrix inequality sets and then based on the model prediction strategy a reset law is derived to minimise a quadratic cost function. When the system states enter into a reset set, according to the computed reset law, the controller states are reset. This method is applied to a typical distillation column to show the effectiveness of the proposed approach and is compared with non-reset control system.