Unknown-input pseudo-state observer synthesis for fractional-order systems: A geometric framework

This paper explores the development and characterization of the invariant subspaces in geometric control theory, namely conditioned invariant, input-containing, unobservability, and detectability subspaces for fractional-order linear systems, and the requirements for the existence of such subspaces have been established. By utilizing these invariance notions, the pseudo-state observation problem in the presence of unknown-inputs for fractional linear systems with Caputo derivative is formulated and solved within the geometric framework for the first time. Furthermore, it is shown that the obtained solubility conditions for the unknown-input pseudo-state observation problem are not confined by the choice of fractional derivative operator. Finally, the applicability and effectiveness of the theoretical findings are further supported by two numerical simulations, including an application to a vehicle suspension system.