Extending the Input and Transformation Space of Different TP Models: An LMI-based Feasibility Analysis

Abstract

This paper discusses that the selection and modification of the input and the transformation space, of the Tensor Product (TP) model representation, of a given quasi– Linear Parameter Varying (qLPV) state‐space model, has an influence on the feasibility regions of the Linear Matrix Inequality (LMI) based control design techniques. Moreover, three factors affect the feasibility regions of the LMI-based control design: The manipulation of the position of vertices The number of the inputs of the TS fuzzy model representation Modifying the transformation space The proof is based on a complex control design example, where the impact of the above factors can be clearly demonstrated. Furthermore, the paper presents that the maximal and minimal parameter space of the controller depends on factors (i) and (ii). The aim of the feasibility test is to show that there exists a solution for LMIs or not, considering these factors. The example is based on the academic Translational Oscillator with Rotational Actuator (TORA) system. Then, the TP model transformation-based framework is used to vary the input space of the TP model representation. In addition, the paper gives a very decisive conclusion that the design technique may be sensitive for the input space of the TS fuzzy model, hence it is necessary to consider the number of inputs, the transformation space and the gains defined on the inputs when a TP model is generated to achieve the best solution to the control purposes. All in all, this paper investigates the effect of input space modification of the TP model representation of a given qLPV state-space model on the feasibility regions of LMI-based controller design methods