Estimation of Regions of Attraction for Nonlinear Systems via Coordinate-Transformed TS Models

Abstract

This paper presents a novel method for estimating larger Region of Attractions (ROAs) for continuous-time nonlinear systems modeled via the Takagi-Sugeno (TS) framework. While classical approaches rely on a single TS representation derived from the original nonlinear system to compute an ROA using Lyapunov-based analysis, the proposed method enhances this process through a systematic coordinate transformation strategy. Specifically, we construct multiple TS models, each obtained from the original nonlinear system under a distinct linear coordinate transformation. Each transformed system yields a local ROA estimate, and the overall ROA is taken as the union of these individual estimates. This strategy leverages the variability introduced by the transformations to reduce conservatism and expand the certified stable region. Numerical examples demonstrate that this approach consistently provides larger ROAs compared to conventional single-model TS-based techniques, highlighting its effectiveness and potential for improved nonlinear stability analysis.