Coordinate transformation of Takagi-Sugeno models: Stability conditions and observer canonical forms

In this paper, Lyapunov-based stability criteria for Takagi-Sugeno models in a new coordinate system are derived. Two different cases are considered: First, a simple change of coordinates with a common similarity transformation matrix for each local model is considered. For this, a linear matrix inequality (LMI) stability criterion for the transformed system based on the original coordinates is presented. Second, a time-variant similarity transformation based on a polytopic set of similarity transformation matrices is studied and a new LMI criterion is proposed to ensure the stability of the transformed Takagi-Sugeno systems. The usefulness of the criterion is shown by numerical examples.