Functional H∞ Filtering for Descriptor Systems with Monotone Nonlinearities

This paper proposes a new framework for the design of functional H∞ filters tailored for nonlinear descriptor systems affected by disturbances. Earliermethods have some significant drawbacks: they rely on the restrictive assumption of system regularity, employ implicit descriptor-form filters that complicate implementation, and emphasize full-order filtering, which is often unnecessary and computationally expensive. To overcome these drawbacks, the proposed filter is developed in an explicit state-space form that allows simple implementation with arbitrary initial conditions. Moreover, its order is minimized by matching it to the dimension of the functional vector, which reduces computational complexity compared to conventional filters. A new set of sufficient conditions is presented for the existence of a functionalH∞ filter, expressed through a rank condition and a linear matrix inequality (LMI) formulation. These conditions guarantee the stability of the estimation error dynamics while ensuring that the L2 gain from disturbances to errors remains below a specified bound. A numerical example based on a simple constrained mechanical system is presented to illustrate the effectiveness of the proposed method.