LMI-based stability analysis and robust controller design for a class of nonlinear chaotic power systems

This paper proposes novel linear matrix inequality (LMI) stability analysis and controller design conditions for nonlinear chaotic power systems. The proposed approach is based on the non-quadratic Lyapunov function (NQLF), non-parallel distributed compensation (non-PDC) schematic and Takagi-Sugeno (TS) fuzzy modeling. Utilizing NQLF causes membership functions (MFs) and their time derivative to appear in the design conditions. To solve this problem, an augmented state vector is proposed which results in removing the MFs and their time derivatives from the design conditions. Moreover, structural constraints on Lyapunov matrices are eliminated. The proposed approach provides relaxed stability analysis and controller design conditions due to the framework that is considered during the formulation derivation. Finally, two practical power systems that exhibit chaotic behaviors are considered to evaluate the proposed approach. Simulation results show advantages of the proposed method compared to the recently published works.