H∞ Filter Design for State Estimation and Unknown Inputs Reconstruction of a Class of Nonlinear systems

We consider a novel method to design a H∞ filter for a class of nonlinear systems subject to unknown inputs. First, we rewrite the system dynamics as a descriptor system. Then, we design a robust H∞ reduced-order filter to estimate both state variables and unknown inputs at the same time. Based on a Lyapunov functional, we derive a sufficient condition for existence of the designed filter which requires solving a nonlinear matrix inequality. The achieved condition is further formulated in terms of a linear matrix inequality (LMI) that is straightforward to solve by popular methods. Finally, the proposed filter is illustrated with an example.