Algebraic pseudo-state estimation for a linear fractional-order time-delay system

This paper studies the non-asymptotic and robust pseudo-state estimation problem for a linear fractional-order time-delay system with multiple proportional delays. To handle the multiple proportional delays, the delay operator is introduced. The considered system is transformed into the fractional-order observer normal form via a bicausal generalized change of coordinates. On this basis, the modulating functions method is applied to derive exact algebraic integral formulas, where novel fractional-order modulating functions are utilized. Then, the original issue can be tackled by the inverse change of coordinates. Finally, a numerical simulation is provided to demonstrate the efficiency and the robustness against noises of the proposed estimator.