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. A power systems case study demonstrates 62% faster convergence and 63% lower steady-state error compared to [1], validated through LMI-based synthesis and adaptive disturbance estimation.