Proportional-derivative unknown input observer design using descriptor system approach for non-minimum phase systems

This paper considers the problem of estimating the state of an MIMO linear system with unknown inputs in the state and output. Through a series of linear transformations in the state and output equations, the original system can be transformed into a descriptor system form. The proposed proportional derivative observer can accurately estimate the system state and avoid the peaking phenomenon. Moreover, the approach developed in this paper does not require the derivatives of the output and can be applied to the system with unstable zeros (with respect to the relation between the output and the unknown input). Finally, our algorithm can prove the valid feasibility and the property of disturbance attenuation through demonstrating a simulation-base example.