Nonlinearity Measure for Nonlinear Dynamic Systems Using a Multimodel Framework

This article is concerned with the assessment of nonlinearity in nonlinear dynamic systems to determine the feasibility of controlling a nonlinear system with either a single linear controller or a multimodel controller. The nonlinear system is decomposed into a bank of linear models, resulting in exploiting the gap metric and the maximum stability margin value of these linear models to introduce two key attributes. The first attribute, termed “slavery quality,” quantifies the behavior of the linear models by examining the feasibility of stabilizing each linear model using other local controllers. In contrast, the second attribute, referred to as “mastery quality,” assesses the ability of each local controller to stabilize the linear systems. The collaboration of the mastery and the slavery qualities not only facilitates assessing the nonlinearity degree of a nonlinear system but also supports the selection of nominal linear models. Three nonlinear systems with different characteristics are investigated. The simulations validate the effectiveness and benefits of the proposed method in understanding the adequacy of a single linear controller or a multimodel controller for a given nonlinear system.