Influence of the Tensor Product Model Representation Of QLPV Models on The Feasibility of Linear Matrix Inequality

Abstract

AbstractThe present paper proves that the vertexes of the tensor product (TP) model type polytopic representation of a given quasi linear parameter varying (qLPV) state‐space model strongly interfere with the feasibility regions of linear matrix inequality (LMI)‐based control design methods. Furthermore this is valid both for the LMI‐based feasibility of the controller and the observer design, but the influence differs for the controller and the observer system components. More specifically, the factors influencing the feasibility regions of the LMI‐based control design include: (i) the manipulation of the vertexes' position; and (ii) the size and complexity of the TP model type polytopic representation, i.e. the number of the vertexes contained in the TP model representation. The proof is based on a complex control design example, where the influence of these factors stated above can be easily and clearly indicated. Furthermore the paper shows via the example that the maximal parameter space of the controller and observer also depends on these factors. The example model consists of the complex Nonlinear Aeroelastic Test Apparatus (NATA) model of the three degree of freedom aeroelastic wing section model including Stribeck friction and the control design method is based on the relaxed TP model transformation‐based control design framework that supports the flexible manipulation of these factors.