Incremental quadratic stability

Luis D'Alto; Martin Corless

doi:10.3934/naco.2013.3.175

Article Contents

2013, Volume 3, Issue 1: 175-201. Doi: 10.3934/naco.2013.3.175

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Incremental quadratic stability

Luis D'Alto^1, and
Martin Corless^2,

1.
Boeing Research and Technology Europe, Avenida Sur del Aeropuerto de Barajas, 38, Edificio 4 Planta, 428042 Madrid
2.
School of Aeronautics and Astronautics, Purdue University, W. Lafayette, IN 47907

Received: February 2012

Revised: December 2012

Published: January 2013

Abstract / Introduction Related Papers Cited by

Abstract

The concept of incremental quadratic stability ($\delta$QS) is very useful in treating systems with persistently acting inputs. To illustrate, if a time-invariant $\delta$QS system is subject to a constant input or $T$-periodic input then, all its trajectories exponentially converge to a unique constant or $T$-periodic trajectory, respectively. By considering the relationship of $\delta$QS to the usual concept of quadratic stability, we obtain a useful necessary and sufficient condition for $\delta$QS. A main contribution of the paper is to consider nonlinear/uncertain systems whose state dependent nonlinear/uncertain terms satisfy an incremental quadratic constraint which is characterized by a bunch of symmetric matrices we call incremental multiplier matrices. We obtain linear matrix inequalities whose feasibility guarantee $\delta$QS of these systems. Frequency domain characterizations of $\delta$QS are then obtained from these conditions. By characterizing incremental multiplier matrices for many common classes of nonlinearities, we demonstrate the usefulness of our results.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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