Output feedback robust stabilization of distributed‐order systems

Abstract This paper addresses the challenge of robust fast stabilization for a class of dynamical systems characterized by slow and ultra‐slow dynamics. The system model is approximated using a distributed‐order derivative of the measured output, which captures the influence of the control input, system dynamics, and external disturbances. The primary objective is to design a controller that ensures robust fast convergence while relying solely on limited structural knowledge of the system and available input‐output data, without requiring direct measurement of the output signal derivatives. Two control strategies are presented: exponential stabilization and finite‐time stabilization. Both approaches employ output feedback control, leveraging a high‐order sliding mode observer based on the Levant non‐recursive exact differentiator for estimating output derivatives and disturbances. The proposed framework ensures reliable state estimation and disturbance rejection, even under modeling uncertainties. Numerical simulations are conducted to validate the proposed methodology, demonstrating a superior performance in ensuring fast stabilization and robustness against disturbances. The results highlight the advantages of the finite‐time stabilization approach in achieving fast convergence while maintaining robust control properties.