Influence of the Tensor Product Model Representation of qLPV Models on the Feasibility of Linear Matrix Inequality Based Stability Analysis

Abstract

The paper investigates and proves the statement, that the convex hull of the polytopic tensor product (TP) model representation influences the feasibility of linear matrix inequality (LMI) based stability analysis methods. The proof is based on a complex stability analysis example of a given quasi linear parameter varying (qLPV) state-space model. Specifically, the three degree of freedom (3-DoF) aeroelastic wing section model including Stribeck friction is used as the tool for the example model. The proof is achieved by utilizing TP model transformation and LMI based tools. As a first step, numerous TP model type control solutions holding different convex hulls are systematically derived of the qLPV model via LMI based control design methods. As a second step, each control solution is further equivalently transformed for different TP model representations holding different convex hulls. Finally, the stability of all solutions over all TP model representations are checked via LMI based stability analysis methods. As a result of the two steps, a two dimensional (2D) convex hull space is attained for the 3-DoF aeroelastic wing section model. The two dimensions are denoted by the LMI based control design and the LMI based stability analysis for different convex hulls. Based on the numerical results, a detailed, comprehensive analysis is provided. The paper as a novelty proves the statement, that the polytopic TP model representation of a given control solution strongly influences the feasibility of LMI based stability analysis methods.

Tensor Product‐Based Model Transformation and Optimal Controller Design for High Order Nonlinear Singularly Perturbed Systems

“…The matrix C k can be determined based on the proposed analytical approach for matrix inversion (47). Finally, we establish the polynomial form of B(x) and H 1 (x)…”

“…Using the Tensor Product many innovational and computationally efficient numerical algorithms have been proposed [38][39][40]. Recently, the tensor product model transformation has received increasing attention because it provides a systematic framework in control design and many analytical approaches can be substituted by more flexible and effective numerical methods, see [41][42][43][44][45][46][47].…”

Tensor Product Model Transformation-based Parallel Distributed Control of Tumor Growth

“…The latest research explored that the LMI based controller design methods are sensitive to the applied convex hulls. Hence, the selection of the applicable convex hull manipulation and the convex hull candidate with respect to the LMI based controller design methods is a critical aspect [31,[41][42][43]. Effective convex hull manipulation techniques are introduced in [35,44,45].…”

Tensor Product Model-based Control Design with Relaxed Stability Conditions for Perching Maneuvers

“…Different types of convex weight functions can be chosen to derive TP model. Proper weight function type would decrease the conservatism of the system [11,[14][15][16][17][18]. Here the interpolation technique [11] is studied to obtain a TP model with less conservatism.…”