Functional H_infity Filtering for Descriptor Systems with Monotone nonlinearities

TL;DR

This paper develops a new method for designing functional H_infinity filters for nonlinear descriptor systems with monotone nonlinearities, using LMIs under a general rank condition, demonstrated on a mechanical system.

Contribution

It introduces a novel LMI-based approach for H_infinity filtering of general descriptor systems with monotone nonlinearities, relaxing regularity assumptions.

Findings

LMI condition guarantees stability and disturbance attenuation

Method successfully applied to a constrained mechanical system

Provides a practical framework for nonlinear descriptor system filtering

Abstract

This paper introduces a novel approach to design of functional H_\infty filters for a class of nonlinear descriptor systems subjected to disturbances. Departing from conventional assumptions regarding system regularity, we adopt a more inclusive approach by considering general descriptor systems that satisfy a rank condition on their coefficient matrices. Under this rank condition, we establish a linear matrix inequality (LMI) as a sufficient criterion ensuring the stability of the error system and constraining the L 2 gain of the mapping from disturbances to errors to a predetermined level. The efficacy of the proposed approach is demonstrated through a practical example involving a simple constrained mechanical system.