Convex Polytopic Modeling of Discrete Time Nonlinear Singularly Perturbed System

Abstract

In this work, the authors propose an analytical and systematic technique to represent the discrete nonlinear singularly perturbed system (SPS) by a coupled state multimodel (MM). This approach is realized without loss of information. This strategy can be applicable to any order SPSs. Another significant characteristic of this technique is to choose between several quasi-LPV forms of the nonlinear system that lead to specific properties of the multiple model structure. Also, the obtained MM has the same state trajectory as the initial nonlinear SPS. Therefore, a set of criteria is provided utilizing the formulation of linear matrix inequality (LMI) to select the most appropriate MM for analysis, observation, or control purposes. A simulation example and a tunnel diode circuit are given to validate the effectiveness of the proposed technique.