2025/07/17 by Artun Sel, Sel, Artun, Mehmet Koruturk +3
Computer Science · Engineering · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Fault Detection and Control Systems #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2507.12718
openalex publication_date 2025/07/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
This paper presents a novel approach for computing enlarged Region of Attractions (ROA) for nonlinear dynamical systems through the integration of multiple coordinate transformations and piecewise quadratic Lyapunov functions within the Takagi-Sugeno (TS) modeling framework. While existing methods typically follow a single-path approach of original system → TS model → ROA computation, the proposed methodology systematically applies a sequence of coordinate transformations to generate multiple system representations, each yielding distinct ROA estimations. Specifically, the approach transforms the original nonlinear system using transformation matrices T1, T2, …, TN to obtain N different coordinate representations, constructs corresponding TS models for each transformed system, and computes individual ROAs using piecewise quadratic Lyapunov functions. The final ROA estimate is obtained as the union of all computed regions, leveraging the flexibility inherent in piecewise quadratic Lyapunov functions compared to traditional quadratic approaches. The enhanced methodology demonstrates significant improvements in ROA size estimation compared to conventional single-transformation techniques, as evidenced through comparative analysis with existing TS-based stability methods.