LMI searches for anticausal and noncausal rational Zames–Falb multipliers

Carrasco, Joaquín; Maya-Gonzalez, Martin; Lanzon, Alexander; Heath, William P.

doi:10.1016/j.sysconle.2014.05.005

Cited by 33 publications

(55 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Optimal design of basis functions is still an open question, and its selection depends on designer's ability. For Zames-Falb multipliers, automatic selection of the poles has been proposed in [38], [55], but their techniques can not be implemented here since they require odd nonlinearities.…”

Section: Methodsmentioning

confidence: 99%

“…A comparison between the rest of the classes for this type of nonlinearity and the class Z is given in [38].…”

Section: Lemma 4 ( [27]mentioning

confidence: 99%

“…For example, if the nonlinearity is slope or sector bounded then Zames-Falb multipliers outperform Lyapunov techniques [28], [38]. In this section, we focus our attention on the absolute stability of a system containing both slope-restricted nonlinearities and constant time delay in an interval [0,…”

Section: A Systems With Saturation and Time Delaymentioning

confidence: 99%

See 2 more Smart Citations

Stability Analysis of Bilateral Teleoperation With Bounded and Monotone Environments via Zames–Falb Multipliers

Tugal

Carrasco

Falcon

et al. 2017

IEEE Trans. Contr. Syst. Technol.

Self Cite

View full text Add to dashboard Cite

Abstract-This paper provides less conservative stability conditions for bilateral teleoperation by exploiting the advantages of the integral quadratic constraint (IQC) framework, where the environment can be defined as a memoryless, bounded, and monotonic nonlinear operator. Recent advances in multiplier theory for appropriate classes of uncertainties/nonlinearities are applied. Since the classes of multipliers have infinite dimension, parametrization of these multipliers is used to obtain convex searches over a finite number of parameters. The stability of the system is analysed as a Lurye system containing timedelay and monotone nonlinearity. As a result, less conservative delay-dependent conditions can be developed. These results are then applied to bilateral teleoperation. Finally, stability results are tested with different experiments; in particular bilateral teleoperation experiments over the internet between Manchester, UK, and Vigo, Spain, have been carried out. The advantage of the proposed approach is demonstrated by reaching higher transparency index for 2-channel position-force teleoperation while ensuring absolute stability.

show abstract

Section: Methodsmentioning

confidence: 99%

“…A comparison between the rest of the classes for this type of nonlinearity and the class Z is given in [38].…”

Section: Lemma 4 ( [27]mentioning

confidence: 99%

See 1 more Smart Citation

Stability Analysis of Bilateral Teleoperation With Bounded and Monotone Environments via Zames–Falb Multipliers

Tugal

Carrasco

Falcon

et al. 2017

IEEE Trans. Contr. Syst. Technol.

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is true for first, second and third-order continuous-time systems (Barabanov, 1988). Thus we know a priori that a third order system is absolutely stable provided φ ∈ S [0, k N ) and we can benchmark a test for stability by seeking the maximum slope value and comparing with this upper bound (e.g Safonov and Wyetzner, 1987;Carrasco et al, 2014b). But the conjecture is false in general and the fourth-order counterexamples proposed more than 40 years ago (Fitts, 1966;O'Shea, 1967;Willems, 1971;Leonov and Kuznetsov, 2013) can also be used as benchmarks as they can be very challenging for stability tests.…”

Section: The Nyquist Value and The Kalman Conjecturementioning

confidence: 99%

“…For this reason, in a series of papers (Turner et al, , 2010Turner and Kerr, 2011;Carrasco et al, 2012a;Turner et al, 2012;Carrasco et al, 2014b) the authors have developed an alternative method for searching for multipliers based on a change of variables similar to that used in H ∞ controller design (Scherer et al, 1997). The main idea is that, if the multiplier is unstructured, but its order is the same as the plant, then a change of variables may be used to "linearise" some of the resulting matrix inequalities.…”

Section: Plant-order Multipliersmentioning

confidence: 99%

Zames-Falb multipliers for absolute stability: From O'Shea's contribution to convex searches

Carrasco

Turner

Heath

2015

2015 European Control Conference (ECC)

View full text Add to dashboard Cite

Absolute stability attracted much attention in the sixties. Several stability conditions for loops with slope-restricted nonlinearities were developed. Results such as the Circle Criterion and the Popov Criterion form part of the core curriculum for students of control. Moreover, the equivalence of results obtained by different techniques, specifically Lyapunov and Popov's stability theories, led to one of the most important results in control engineering: the KYP Lemma.For Lurye 1 systems this work culminated in the class of multipliers proposed by O'Shea in 1966 and formalised by Zames and Falb in 1968. The superiority of this class was quickly and widely accepted. Nevertheless the result was ahead of its time as graphical techniques were preferred in the absence of readily available computer optimization. Its first systematic use as a stability criterion came twenty years after the initial proposal of the class. A further twenty years have been required to develop a proper understanding of the different techniques that can be used. In this long gestation some significant knowledge has been overlooked or forgotten. Most significantly, O'Shea's contribution and insight is no longer acknowledged; his papers are barely cited despite his original parameterization of the class.This tutorial paper aims to provide a clear and comprehensive introduction to the topic from a user's viewpoint. We review the main results: the stability theory, the properties of the multipliers (including their phase properties, phase-equivalence results and the issues associated with causality), and convex searches. For clarity of exposition we restrict our attention to continuous time multipliers for single-input single-output results. Nevertheless we include several recent significant developments by the authors and others. We illustrate all these topics using an example proposed by O'Shea himself.

show abstract

Modified static anti-windup for saturated systems with sector-bounded and slope-restricted nonlinearities

Wang

Pei

Tang

2016

Int. J. Robust. Nonlinear Control

View full text Add to dashboard Cite

SUMMARYThis paper proposes modified static anti-windup techniques for saturated systems with sector-bounded and slope-restricted nonlinearities by augmenting the pre-designed controller with the so-called differential compensator to process the slope restriction. By using a purely quadratic Lyapunov function and with a modified sector condition dealing with actuator saturation, LMI-based synthesis conditions are presented to address the problems of the estimates of the region of attraction and L 2 performance analysis of the closed-loop system. Numerical examples illustrate the effectiveness of the proposed approaches.

show abstract

LMI searches for anticausal and noncausal rational Zames–Falb multipliers

Cited by 33 publications

References 21 publications

Stability Analysis of Bilateral Teleoperation With Bounded and Monotone Environments via Zames–Falb Multipliers

Stability Analysis of Bilateral Teleoperation With Bounded and Monotone Environments via Zames–Falb Multipliers

Zames-Falb multipliers for absolute stability: From O'Shea's contribution to convex searches

Modified static anti-windup for saturated systems with sector-bounded and slope-restricted nonlinearities

Contact Info

Product

Resources

About