Robust observer for multiple time-delay systems with unknown inputs

This work proposes a new design of a full-order observer able to achieve reconstruction of the state vector of LTI multivariable systems with multiple time-delays and unknown inputs (UI). The basic idea is to transform the problem of the unknown input observer (UIO) for LTI multivariable systems with multiple time delays to that of a standard one. The observer algorithm is achieved in three stages. First, the LTI multivariable system with multiple delays and UI is transformed into a distributed parameter system (DPS) described by linear partial differential equations (PDEs). Then, using the orthogonal collocation method, the DPS is reduced in a lumped system described by linear ordinary differential equations (ODE). Finally, the problem of the UIO design for the reduced system is solved. The efficiency of the proposed algorithm is finally illustrated using the non-minimum phase model of the 4-tank benchmark.