A systematic decomposition approach of nonlinear systems by combining gap metric and stability margin

In this paper, in order to control a nonlinear dynamic system via multi-model controller, we propose a systematic approach to determine the nominal local linear models. These models are selected from the local models bank and results in a reduced nominal models set that provides enough information to design a multi-model controller. To determine the initial local models bank, gap metric is used so that the distance between two successive local models is smaller than a threshold value. Then, a systematic approach that aims to get a reduced nominal models bank is developed. Based on this approach, first, a binary gap matrix is defined by combining gap metric and stability information. Then, several rows of this matrix are selected such that the sum of them becomes a non-zero vector. The proposed approach along with a designed robust controller is validated on a pH neutralization regarding to its highly nonlinear behavior.