Fault Reconstruction for Lipschitz Nonlinear Descriptor Systems via Linear Matrix Inequality Approach

Abstract

By using the linear matrix inequality for a nonlinear descriptor system with a Lipschitz constraint, a state-space observer is designed to simultaneously reconstruct the descriptor system states and the fault signals. For a nonlinear descriptor system with bounded input disturbances, a robust state-space observer is proposed to simultaneously reconstruct the descriptor system states and the faults and attenuate the input bounded disturbances. The fault considered can be unbounded (provided that the qth derivative of the fault is zero piecewise or norm bounded); thus, the present fault reconstruction approach can handle a large class of fault signals including time-invariant and time-varying signals. A numerical example is given to illustrate the proposed design approach.