Extracting LPV and qLPV Structures From State-Space Functions: A TP Model Transformation Based Framework

Abstract

This paper proposes a tensor product (TP) model transformation-based framework requiring minimal human intuition to numerically reconstruct linear time invariant, Takagi–Sugeno (T–S) fuzzy model-based linear parameter varying and quasi-linear parameter varying representations of state-space models. The proposed framework facilitates the manipulation of the structure of the system matrix, the parameter vector—including state elements—and the vertex systems. The motivation behind this capability is that all of these structural components strongly influence the control design and the resulting control performance. An important feature of the framework is that it is agnostic towards the formulation of the state-space model, i.e., whether it is given using soft-computing-based techniques or closed formulae. The proposed approach is an extension of the TP model-based control design framework and inherits all of its advantageous properties, e.g., it can be easily used to find minimal representations, including the higher order singular value-based canonical form, and it supports the clear formulation of complexity/accuracy tradeoffs and allows for conversions to various types of convex representations, making for a flexible way to manipulate the weighting and antecedent functions. This paper gives examples to show how the framework can be used in a routine-like fashion and to highlight how it can be applied to the problem of finding useful T–S fuzzy model variations of a given model.