Frequency Response Functions for Nonlinear Convergent Systems

Pavlov, Alexey; Wouw, Nathan van de; Nijmeijer, Henk

doi:10.1109/tac.2007.899020

Cited by 98 publications

(84 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Similarly, these conditions ensure that the response to a constant input also tends to a constant value. These features pave the way towards a nonlinear frequency analysis, with the notion of nonlinear Bode plot [21]. Our results are valid for a wide class of nonlinear time-delayed systems, and allow for multiple and time-varying delays, as long as they are upper-bounded by a known constant.…”

Section: Introductionmentioning

confidence: 64%

A Razumikhin approach for the incremental stability of delayed nonlinear systems

Chaillet¹,

Pogromsky

Rüffer

2013

52nd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

Abstract-This paper provides sufficient conditions for the incremental stability of time-delayed nonlinear systems. It relies on the Razumikhin-Lyapunov approach, which consists in invoking small-gain arguments by treating the delayed state as a feedback perturbation. The results are valid for multiple delays, as well as bounded time-varying delays. We provide conditions under which the limit solution of a time-delayed nonlinear system in response to a periodic (resp. constant) input is itself periodic and of the same period (resp. constant). As an illustration, a specific focus is given on a class of delayed Lur'e systems.

show abstract

Section: Introductionmentioning

confidence: 64%

A Razumikhin approach for the incremental stability of delayed nonlinear systems

Chaillet¹,

Pogromsky

Rüffer

2013

52nd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

show abstract

“…. 1] T ∈ R m and some α > 0, ω > 0, let ν : R 2 + → R + be the output frequency response map for (1) and (2) (see [25] for such function de¦nition for the class of convergent systems; for generic case, such type of maps can be introduced using the theory of Cauchy gains and asymptotic amplitudes [26]), i. e., lim t→+∞ |Ce(t)| ≤ ν(α, ω) . Corollary 1.…”

Section: Performance Optimizationmentioning

confidence: 99%

Nonlinear observer techniques for oscillatory failure case detection

Efimov

Zolghadri

2013

Progress in Flight Dynamics, Guidance, Navigation, Control, Fault Detection, and Avionics

View full text Add to dashboard Cite

The problem of observer design for fault detection in a class of nonlinear systems subject to parametric and signal uncertainties is studied. The design procedure includes formalized optimization of observer free parameters in terms of trade-o¨s for fault detection performance and robustness to external disturbances or model uncertainties. The technique makes use of some monotonicity conditions imposed on the estimation error dynamics. E©ciency of the proposed approach is demonstrated through the Oscillatory Failure Case (OFC) in aircraft control surface servoloops.

show abstract

“…Some works addressing such stability properties for classes of nonsmooth systems can be found in [16], [17], [21], [22], [23], [25]. Results on incremental stability for hybrid dynamical systems are rare.…”

Section: Introductionmentioning

confidence: 99%

Definitions of incremental stability for hybrid systems

Biemond

Heemels

Wouw

2015

2015 54th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

Abstract-The analysis of incremental stability properties typically involves measuring the distance between any pair of solutions of a given dynamical system, corresponding to different initial conditions, at the same time instant. This approach is not directly applicable for hybrid systems in general. Indeed, hybrid systems generate solutions that are defined with respect to hybrid times, which consist of both the continuous time elapsed and the discrete time, that is the number of jumps the solution has experienced. Two solutions of a hybrid system do not a priori have the same time domain, and we may therefore not be able to compare them at the same hybrid time instant. To overcome this issue, we invoke graphical closeness concepts. We present definitions for incremental stability depending on whether incremental asymptotic stability properties hold with respect to the hybrid time, the continuous time, or the discrete time, respectively. Examples are provided throughout the paper to illustrate these definitions, and the relations between these three incremental stability notions are investigated. The definitions are shown to be consistent with those available in the literature for continuous-time and discrete-time systems.

show abstract

Frequency Response Functions for Nonlinear Convergent Systems

Cited by 98 publications

References 16 publications

A Razumikhin approach for the incremental stability of delayed nonlinear systems

A Razumikhin approach for the incremental stability of delayed nonlinear systems

Nonlinear observer techniques for oscillatory failure case detection

Definitions of incremental stability for hybrid systems

Contact Info

Product

Resources

About