IEICE TRANSACTIONS on Fundamentals
Using Sum of Squares Decomposition for Stability of Hybrid Systems
Summary :
This paper deals with stability analysis of hybrid systems. Such systems are characterized by a combination of continuous dynamics and logic based switching between discrete modes. Lyapunov theory is a well known methodology for the stability analysis of linear and nonlinear systems in control system literature. Construction of Lyapunov functions for hybrid systems is generally a difficult task, but once these functions are defined, stabilization of the system is straight-forward. The sum of squares (SOS) decomposition and semidefinite programming has also provided an efficient methodology for analysis of nonlinear systems. The computational method used in this paper relies on the SOS decomposition of multivariate polynomials. By using SOS, we construct a (some) Lyapunov function(s) for the hybrid system. The reduction techniques provide numerical solution of large-scale instances; otherwise they will be practically unsolvable. The introduced method can be used for hybrid systems with linear or nonlinear vector fields. Some examples are given to demonstrate the capabilities of the proposed approach.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.11 pp.2478-2487
- Publication Date
- 2007/11/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e90-a.11.2478
- Type of Manuscript
- Special Section PAPER (Special Section on Concurrent/Hybrid Systems: Theory and Applications)
- Category
Authors
Keyword
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Mohammad Ali BADAMCHIZADEH, Sohrab KHANMOHAMMADI, Ghasem ALIZADEH, Ali AGHAGOLZADEH, Ghader KARIMIAN, "Using Sum of Squares Decomposition for Stability of Hybrid Systems" in IEICE TRANSACTIONS on Fundamentals,
vol. E90-A, no. 11, pp. 2478-2487, November 2007, doi: 10.1093/ietfec/e90-a.11.2478.
Abstract: This paper deals with stability analysis of hybrid systems. Such systems are characterized by a combination of continuous dynamics and logic based switching between discrete modes. Lyapunov theory is a well known methodology for the stability analysis of linear and nonlinear systems in control system literature. Construction of Lyapunov functions for hybrid systems is generally a difficult task, but once these functions are defined, stabilization of the system is straight-forward. The sum of squares (SOS) decomposition and semidefinite programming has also provided an efficient methodology for analysis of nonlinear systems. The computational method used in this paper relies on the SOS decomposition of multivariate polynomials. By using SOS, we construct a (some) Lyapunov function(s) for the hybrid system. The reduction techniques provide numerical solution of large-scale instances; otherwise they will be practically unsolvable. The introduced method can be used for hybrid systems with linear or nonlinear vector fields. Some examples are given to demonstrate the capabilities of the proposed approach.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.11.2478/_p
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@ARTICLE{e90-a_11_2478,
author={Mohammad Ali BADAMCHIZADEH, Sohrab KHANMOHAMMADI, Ghasem ALIZADEH, Ali AGHAGOLZADEH, Ghader KARIMIAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Using Sum of Squares Decomposition for Stability of Hybrid Systems},
year={2007},
volume={E90-A},
number={11},
pages={2478-2487},
abstract={This paper deals with stability analysis of hybrid systems. Such systems are characterized by a combination of continuous dynamics and logic based switching between discrete modes. Lyapunov theory is a well known methodology for the stability analysis of linear and nonlinear systems in control system literature. Construction of Lyapunov functions for hybrid systems is generally a difficult task, but once these functions are defined, stabilization of the system is straight-forward. The sum of squares (SOS) decomposition and semidefinite programming has also provided an efficient methodology for analysis of nonlinear systems. The computational method used in this paper relies on the SOS decomposition of multivariate polynomials. By using SOS, we construct a (some) Lyapunov function(s) for the hybrid system. The reduction techniques provide numerical solution of large-scale instances; otherwise they will be practically unsolvable. The introduced method can be used for hybrid systems with linear or nonlinear vector fields. Some examples are given to demonstrate the capabilities of the proposed approach.},
keywords={},
doi={10.1093/ietfec/e90-a.11.2478},
ISSN={1745-1337},
month={November},}
Copy
TY - JOUR
TI - Using Sum of Squares Decomposition for Stability of Hybrid Systems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2478
EP - 2487
AU - Mohammad Ali BADAMCHIZADEH
AU - Sohrab KHANMOHAMMADI
AU - Ghasem ALIZADEH
AU - Ali AGHAGOLZADEH
AU - Ghader KARIMIAN
PY - 2007
DO - 10.1093/ietfec/e90-a.11.2478
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2007
AB - This paper deals with stability analysis of hybrid systems. Such systems are characterized by a combination of continuous dynamics and logic based switching between discrete modes. Lyapunov theory is a well known methodology for the stability analysis of linear and nonlinear systems in control system literature. Construction of Lyapunov functions for hybrid systems is generally a difficult task, but once these functions are defined, stabilization of the system is straight-forward. The sum of squares (SOS) decomposition and semidefinite programming has also provided an efficient methodology for analysis of nonlinear systems. The computational method used in this paper relies on the SOS decomposition of multivariate polynomials. By using SOS, we construct a (some) Lyapunov function(s) for the hybrid system. The reduction techniques provide numerical solution of large-scale instances; otherwise they will be practically unsolvable. The introduced method can be used for hybrid systems with linear or nonlinear vector fields. Some examples are given to demonstrate the capabilities of the proposed approach.
ER -
English
