Synthesis of functional unknown input observers for MIMO systems with arbitrary relative degree

This paper addresses the design of functional unknown input observers for multi-input multi-output linear time-invariant systems. In contrast to many existing approaches, the proposed method is applicable to systems with arbitrary relative degree, which significantly enlarges the class of admissible plants. Explicit algebraic conditions are derived for the existence of the observer and for the selection of the matrix defining the reconstructible linear combinations of the state variables. A constructive synthesis procedure is developed. The applicability of the proposed framework is further illustrated for a class of nonlinear systems with additive nonlinearities treated as unknown inputs. Simulation results confirm the effectiveness of the developed observers and demonstrate accurate estimation in the presence of uncertainty.