Homogeneous piecewise polynomial Lyapunov function for robust stability of uncertain piecewise linear system

BenAbdallah, Abdallah; Hammami, Mohamed Ali; Kallel, Jalel

doi:10.1063/1.3106474

Title: Homogeneous piecewise polynomial Lyapunov function for robust stability of uncertain piecewise linear system

Full Record
Other Related Research

Abstract

In this paper we present some sufficient conditions for the robust stability and stabilization of time invariant uncertain piecewise linear system using homogenous piecewise polynomial Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities which can be numerically solved. An application of the obtained result is given. It consists in resolving the stabilization of piecewise uncertain linear control systems by using a state piecewise linear feedback.

Authors:

BenAbdallah, Abdallah ^[1]; Hammami, Mohamed Ali ^[2]; Kallel, Jalel ^[3]

Institut superieur d'informatique et multimedia de Sfax BP 242-3021 (Tunisia)
Faculty of Sciences of Sfax, BP 802-3018 Sfax (Tunisia)
Institut preparatoire aux etudes d'ingenieurs de Sfax BP 1172-3018 (Tunisia)

Publication Date:: Thu Mar 05 00:00:00 EST 2009

OSTI Identifier:: 21293324

Resource Type:: Journal Article

Journal Name:: AIP Conference Proceedings

Additional Journal Information:: Journal Volume: 1107; Journal Issue: 1; Conference: CISA'09: 2. Mediterranean conference on intelligent systems and automation, Zarzis (Tunisia), 23-25 Mar 2009; Other Information: DOI: 10.1063/1.3106474; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CONTROL; CONTROL SYSTEMS; FEEDBACK; LYAPUNOV METHOD; MATRICES; NONLINEAR PROBLEMS; POLYNOMIALS; STABILITY; STABILIZATION

Citation Formats


                    BenAbdallah, Abdallah, Hammami, Mohamed Ali, and Kallel, Jalel. Homogeneous piecewise polynomial Lyapunov function for robust stability of uncertain piecewise linear system.  United States: N. p., 2009. 
        Web.  doi:10.1063/1.3106474.

Copy to clipboard


                    BenAbdallah, Abdallah, Hammami, Mohamed Ali, & Kallel, Jalel. Homogeneous piecewise polynomial Lyapunov function for robust stability of uncertain piecewise linear system.  United States.  https://doi.org/10.1063/1.3106474

Copy to clipboard


                    BenAbdallah, Abdallah, Hammami, Mohamed Ali, and Kallel, Jalel. 2009.  
        "Homogeneous piecewise polynomial Lyapunov function for robust stability of uncertain piecewise linear system".  United States.  https://doi.org/10.1063/1.3106474.

Copy to clipboard


                    
@article{osti_21293324,

  title        = {Homogeneous piecewise polynomial Lyapunov function for robust stability of uncertain piecewise linear system},

  author       = {BenAbdallah, Abdallah and Hammami, Mohamed Ali and Kallel, Jalel},

  abstractNote = {In this paper we present some sufficient conditions for the robust stability and stabilization of time invariant uncertain piecewise linear system using homogenous piecewise polynomial Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities which can be numerically solved. An application of the obtained result is given. It consists in resolving the stabilization of piecewise uncertain linear control systems by using a state piecewise linear feedback.},

  doi          = {10.1063/1.3106474},

  url          = {https://www.osti.gov/biblio/21293324},
  journal      = {AIP Conference Proceedings},

  issn         = {0094-243X},

  number       = 1,

  volume       = 1107,

  place        = {United States},

  year         = {Thu Mar 05 00:00:00 EST 2009},

  month        = {Thu Mar 05 00:00:00 EST 2009}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1063/1.3106474

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

H{sub ∞} memory feedback control for uncertain singular Markov jump systems with time-varying delay and input saturation

Journal Article Fu, Lei; Ma, Yuechao - Computational and Applied Mathematics

This paper concerns with the H{sub ∞} robust exponential stability and memory state feedback stabilization of singular Markov jump systems with time-delay and input saturation. Linear matrix inequality conditions are given to guarantee regularity, impulse-freeness and exponential stability for the singular Markov jump system. Moreover, sufficient conditions are presented to ensure the H{sub ∞} disturbance attenuation level, and the design method of memory feedback controller is developed by solving linear matrix inequalities optimization problem without any decompositions of system matrices and equivalent transformation. Furthermore, the function in the proof procedure belongs to multiple Lyapunov-like functions whose advantage lies in theirmore »« less
https://doi.org/10.1007/S40314-018-0595-5
Composite Robust $$H_\infty$$ Control for Uncertain Stochastic Nonlinear Systems with State Delay via Disturbance Observer

Journal Article Liu, Yunlong; Wang, Hong; Guo, Lei - IEEE Transactions on Automatic Control

In this paper, the robust stochastic stabilization and robust H1 control problems are investigated for uncertain stochastic time-delay systems with nonlinearity and multiple disturbances. By estimating the disturbance, which can be described by an exogenous model, in control input channel, a composite control scheme is proposed by integrating the output of the disturbance observer with state feedback control law. Sufficient conditions for the existence of the disturbance observer and composite controller are established in terms of linear matrix inequalities, which ensure the mean-square asymptotic stability of the resulting closed-loop system and the disturbance attenuation and disturbance rejection performance can bemore »« less
https://doi.org/10.1109/TAC.2018.2819683
Composite Robust $$H_\infty$$ Control for Uncertain Stochastic Nonlinear Systems with State Delay via Disturbance Observer

Journal Article Liu, Yunlong; Wang, Hong; Guo, Lei - IEEE Transactions on Automatic Control

Here in this note, the robust stochastic stabilization and robust H_infinity control problems are investigated for uncertain stochastic time-delay systems with nonlinearity and multiple disturbances. By estimating the disturbance, which can be described by an exogenous model, a composite hierarchical control scheme is proposed that integrates the output of the disturbance observer with state feedback control law. Sufficient conditions for the existence of the disturbance observer and composite hierarchical controller are established in terms of linear matrix inequalities, which ensure the mean-square asymptotic stability of the resulting closed-loop system and the disturbance attenuation. It has been shown that the disturbancemore »« less
Cited by 24
https://doi.org/10.1109/TAC.2018.2819683

Full Text Available
Robust stabilization via computer-generated Lyapunov functions: An application to a magnetic levitation system

Conference Blanchini, F; Carabelli, S

We apply a technique recently proposed in literature for the robust stabilization of linear systems with time-varying uncertain parameters to a magnetic levitation system. This technique allows the construction of a polyhedral Lyapunov function and a linear variable-structure stabilizing controller.
Stability of moving invariant sets and uncertain dynamic systems on time scales

Conference Lakshmikantham, V; Sivasundaram, S

Nonlinear differential equations with uncertain parameters may cause change of equilibrium-states. To investigate such situations, Siljak, Ikeda and Ohata have introduced the notion of parametric stability and discussed its study which is interesting in itself. A fundamental feedback control problem is that of obtaining some desired behavior from the given system which has uncertain information. Leitmann and associates have dealt with such a problem in a series of papers. They have investigated continuous and discrete uncertain systems by means of Lyapunov functions. Recently, a theory known as dynamic systems on time scales has been built which incorporates both continuous andmore »« less

Similar Records