A New Method to Reduce the Multi-Model Set Based on Maximum Stability Margin and Gap Metric

In this paper the multiple model control of linear time invariant systems with wide uncertainty is studied and a new straightforward and systematic method is proposed to select the local models. The gap metric is used to measure the distance between local models and the maximum stability margin is employed to grid the uncertainty space and measure the permissible distance between local models. The proposed method guarantees the improvement of the maximum stability margin which has direct influence on the reduction of the number of local models and computational complexity loads. To evaluate performance of the proposed method, control of a mass-spring-dashpot system is considered and it is shown that based on our algorithm only a single local model is adequate to control this system while the existing methods in the literature require five local models.