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Verification of ISS, iISS and IOSS properties applying weighted homogeneity

Emmanuel Bernuau, +4 more
- 01 Dec 2013 - 
- Vol. 62, Iss: 12, pp 1159-1167
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TLDR
Several conditions are proposed to check different robustness properties for generic nonlinear systems applying the weighted homogeneity concept and it is shown that, under some mild conditions, the system robustness can be established as a function of the degree of homogeneity.
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This article is published in Systems & Control Letters.The article was published on 2013-12-01 and is currently open access. It has received 130 citations till now.

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Citations
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Journal ArticleDOI

On homogeneity and its application in sliding mode control

Emmanuel Bernuau, +3 more
- 01 Apr 2014 - 
TL;DR: Within this framework, most of the popular high-order sliding mode control schemas are analysed and some recently obtained results about homogeneity for differential inclusions and robustness with respect to perturbations in the context of input-to-state stability are stressed.
Journal ArticleDOI

Robust Stabilization of MIMO Systems in Finite/Fixed Time

Andrey Polyakov, +2 more
- 10 Jan 2016 - 
TL;DR: In this article, a control design algorithm based on block decomposition and Implicit Lyapunov Function (ILF) technique is developed for finite-time and fixed-time stabilization of linear multi-input system with nonlinear uncertainties and disturbances.
Journal ArticleDOI

Finite-time and fixed-time observer design: Implicit Lyapunov function approach

Francisco Lopez-Ramirez, +5 more
- 01 Jan 2018 - 
TL;DR: The proposed nonlinear dynamic observers guarantee convergence of the observer states to the original system state in a finite and in a fixed (defined a priori ) time.
Journal ArticleDOI

Homogeneous High Order Sliding Mode design: A Lyapunov approach

Emmanuel Cruz-Zavala, +1 more
- 01 Jun 2017 - 
TL;DR: A large and simply parametrized family of “usual” discontinuous and quasi-continuous HOSM controllers of nested and polynomial type are obtained, that share the robustness and accuracy properties of the existing ones.
Journal ArticleDOI

Super-Twisting Algorithm in presence of time and state dependent perturbations

Ismael Castillo, +2 more
- 02 Nov 2018 - 
TL;DR: A non-smooth strict Lyapunov function is used to obtain the conditions for the global finite-time stability and to estimate the time of convergence of the generalized Super-Twisting Algorithm.
References
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Journal ArticleDOI

Finite-Time Stability of Continuous Autonomous Systems

Sanjay P. Bhat, +1 more
- 01 Feb 2000 - 
TL;DR: It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related and converse Lyap Unov results can only assure the existence of continuous Lyap unov functions.
Journal ArticleDOI

Dissipative dynamical systems part I: General theory

Jan C. Willems
- 01 Jan 1972 - 
TL;DR: In this paper, a general theory of dissipative dynamical systems is presented, where dissipativeness is defined in terms of an inequality involving the storage function and the supply function, which is bounded from below by the available storage and from above by the required supply.
Journal ArticleDOI

Smooth stabilization implies coprime factorization

Eduardo D. Sontag
- 01 Jan 1989 - 
TL;DR: In this paper, it was shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system.
Book

L2-Gain and Passivity Techniques in Nonlinear Control

A.J. van der Schaft
TL;DR: In this article, a small gain and passivity of input-output maps are discussed. But the authors focus on the Hamiltonian system as passive systems and do not consider the Hamilton-Jacobi Inequalities.
Journal ArticleDOI

Continuous finite-time stabilization of the translational and rotational double integrators

Sanjay P. Bhat, +1 more
- 01 May 1998 - 
TL;DR: A class of bounded continuous time-invariant finite-time stabilizing feedback laws is given for the double integrator because Lyapunov theory is used to prove finite- time convergence.
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- 01 Jun 2008 - 

Homogeneous Lyapunov function for homogeneous continuous vector field

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- 01 Dec 1992 - 

Homogeneity approach to high-order sliding mode design

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Frequently Asked Questions (1)
Q1. What are the contributions in "Verification of iss, iiss and ioss properties applying weighted homogeneity" ?

In this paper, several conditions are proposed to check different robustness properties ( ISS, iISS, IOSS and OSS ) for generic nonlinear systems applying the weighted homogeneity concept ( global or local ).