Regular Papers

International Journal of Control, Automation and Systems 2009; 7(3): 331-339

Published online May 30, 2009

https://doi.org/10.1007/s12555-009-0301-x

© The International Journal of Control, Automation, and Systems

Stability of Nonlinear Hybrid Dynamical Systems with Time Delay via

Mohammad Ali Badamchizadeh, Sohrab Khanmohammadi, Gasem Alizadeh, and Ali Aghagolzadeh

University of Tabriz, Iran

Abstract

Considering an infinite number of eigenvalues for time delay systems, it is difficult to determine their stability. We have developed a new approach for the stability test of time delay nonlinear hybrid systems. Construction of Lyapunov functions for hybrid systems is generally a difficult task, but once these functions are found, stability’s analysis of the system is straight-forward. In this paper both delay-independent and delay-dependent stability tests are proposed, based on the construction of ap-propriate Lyapunov-Krasovskii functionals. The methodology is based on the sum of squares decom-position of multivariate polynomials and the algorithmic construction is achieved through the use of semidefinite programming. The reduction techniques provide numerical solution of large-scale in-stances; otherwise they will be computationally infeasible to solve. The introduced method can be used for hybrid systems with linear or nonlinear vector fields. Finally simulation results show the correct-ness and validity of the designed method.

Keywords Hybrid systems, semidefinite programming, stability, sum of square, time delay.

Article

Regular Papers

International Journal of Control, Automation and Systems 2009; 7(3): 331-339

Published online June 1, 2009 https://doi.org/10.1007/s12555-009-0301-x

Copyright © The International Journal of Control, Automation, and Systems.

Stability of Nonlinear Hybrid Dynamical Systems with Time Delay via

Mohammad Ali Badamchizadeh, Sohrab Khanmohammadi, Gasem Alizadeh, and Ali Aghagolzadeh

University of Tabriz, Iran

Abstract

Considering an infinite number of eigenvalues for time delay systems, it is difficult to determine their stability. We have developed a new approach for the stability test of time delay nonlinear hybrid systems. Construction of Lyapunov functions for hybrid systems is generally a difficult task, but once these functions are found, stability’s analysis of the system is straight-forward. In this paper both delay-independent and delay-dependent stability tests are proposed, based on the construction of ap-propriate Lyapunov-Krasovskii functionals. The methodology is based on the sum of squares decom-position of multivariate polynomials and the algorithmic construction is achieved through the use of semidefinite programming. The reduction techniques provide numerical solution of large-scale in-stances; otherwise they will be computationally infeasible to solve. The introduced method can be used for hybrid systems with linear or nonlinear vector fields. Finally simulation results show the correct-ness and validity of the designed method.

Keywords: Hybrid systems, semidefinite programming, stability, sum of square, time delay.

IJCAS
July 2024

Vol. 22, No. 7, pp. 2055~2340

Stats or Metrics

Share this article on

  • line

Related articles in IJCAS

IJCAS

eISSN 2005-4092
pISSN 1598-6446