Output Tracking Control Design for Nonlinear Systems Represented by Polytopic Linear Models

In this paper, modeling, analyzing and controlling nonlinear systems using Polytopic linear models is considered. First, the output tracking problem is investigated for the state of the system as compared to the affine input, and then the problem is solved for the non-affine state. In the state of determining the parameters of each region to increase the problem solving speed we determine the weighted function in a specific manner that prevents interference between the regions and by solving an linear inequality matrix of controller design , in contrast to the past, it is not necessary to solve a bilinear matrix inequality and only by solving a linear one, the controller will be designed. To stability and design of the controller, a method is used to ensure both the stability of the approximate model (polytopic) and the stability of the main model (nonlinear). Finally, the results are taken and the methods proposed are used to  design of an elastic missile  system.