Adaptive Observer Design with Fixed-Time Convergence, Online Disturbance Learning, and Low-Conservatism Linear Matrix Inequalities for Time-Varying Perturbed Systems

This paper proposes a finite-time adaptive observer with online disturbance learning for time-varying disturbed systems. By integrating parameter-dependent Lyapunov functions and slack matrix techniques, the method eliminates conservative static disturbance bounds required in prior work while guaranteeing fixed-time convergence. The proposed approach features a non-diagonal gain structure that provides superior noise rejection capabilities, demonstrating 41% better performance under measurement noise compared to conventional methods. A power systems case study demonstrates significantly improved performance, including 62% faster convergence and 63% lower steady-state error. These results are validated through LMI-based synthesis and adaptive disturbance estimation. Implementation analysis confirms the method’s feasibility for real-time systems with practical computational requirements.