L2 Observers for a Class of Nonlinear Systems with Unknown Inputs

TL;DR

This paper develops L2 observers for nonlinear systems with unknown inputs, providing LMI-based gain design and conditions for arbitrarily small error norms, applicable to a broad class of nonlinearities.

Contribution

It introduces a novel LMI-based observer design method for nonlinear systems with unknown inputs, ensuring certified L2 performance and small error bounds.

Findings

LMI conditions for observer gain design are derived.

Feasibility conditions for the LMIs are established.

Method guarantees arbitrarily small error norms under certain conditions.

Abstract

We consider the problem of estimating the state and unknown input for a large class of nonlinear systems subject to unknown exogenous inputs. The exogenous inputs themselves are modeled as being generated by a nonlinear system subject to unknown inputs. The nonlinearities considered in this work are characterized by multiplier matrices that include many commonly encountered nonlinearities. We obtain a linear matrix inequality (LMI), that, if feasible, provides the gains for an observer which results in certified L2 performance of the error dynamics associated with the observer. We also present conditions which guarantee that the L2 norm of the error can be made arbitrarily small and investigate conditions for feasibility of the proposed LMIs.