Control vector lyapunov functions for large-scale impulsive dynamical systems.

Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we provide generalizations to the recent extensions of vector Lyapunov theory for continuous-time systems to address stability and control design of impulsive dynamical systems via vector Lyapunov functions. Specifically, we provide a generalized comparison principle involving hybrid comparison dynamics that are dependent on comparison system states as well as the nonlinear impulsive dynamical system states. Furthermore, we develop stability results for impulsive dynamical systems that involve vector Lyapunov functions and hybrid comparison inequalities. Based on these results, we show that partial stability for state-dependent impulsive dynamical systems can be addressed via vector Lyapunov functions. Furthermore, we extend the novel notion of control vector Lyapunov functions to impulsive dynamical systems. Using control vector Lyapunov functions, we present a universal decentralized feedback stabilizer for a decentralized affine in the control nonlinear impulsive dynamical system. These results are then used to develop decentralized controllers for large-scale impulsive dynamical systems with robustness guarantees against full modeling uncertainty.

Main Author: Nersesov, Sergey.
Other Authors: Haddad, Wassim.
Format: Villanova Faculty Authorship
Language: English
Published: 2006
Online Access: http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:178286
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dc_source_str_mv Proceedings of the 45th IEEE Conference on Decision & Control, Manchester Grand Hyatt Hotel, San Diego, CA, USA, December 13-15, 2006, pg. 4813-4820.
author Nersesov, Sergey.
author_facet_str_mv Nersesov, Sergey.
Haddad, Wassim.
author_or_contributor_facet_str_mv Nersesov, Sergey.
Haddad, Wassim.
author_s Nersesov, Sergey.
spellingShingle Nersesov, Sergey.
Control vector lyapunov functions for large-scale impulsive dynamical systems.
author-letter Nersesov, Sergey.
author_sort_str Nersesov, Sergey.
author2 Haddad, Wassim.
author2Str Haddad, Wassim.
dc_title_str Control vector lyapunov functions for large-scale impulsive dynamical systems.
title Control vector lyapunov functions for large-scale impulsive dynamical systems.
title_short Control vector lyapunov functions for large-scale impulsive dynamical systems.
title_full Control vector lyapunov functions for large-scale impulsive dynamical systems.
title_fullStr Control vector lyapunov functions for large-scale impulsive dynamical systems.
title_full_unstemmed Control vector lyapunov functions for large-scale impulsive dynamical systems.
collection_title_sort_str control vector lyapunov functions for large-scale impulsive dynamical systems.
title_sort control vector lyapunov functions for large-scale impulsive dynamical systems.
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description Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we provide generalizations to the recent extensions of vector Lyapunov theory for continuous-time systems to address stability and control design of impulsive dynamical systems via vector Lyapunov functions. Specifically, we provide a generalized comparison principle involving hybrid comparison dynamics that are dependent on comparison system states as well as the nonlinear impulsive dynamical system states. Furthermore, we develop stability results for impulsive dynamical systems that involve vector Lyapunov functions and hybrid comparison inequalities. Based on these results, we show that partial stability for state-dependent impulsive dynamical systems can be addressed via vector Lyapunov functions. Furthermore, we extend the novel notion of control vector Lyapunov functions to impulsive dynamical systems. Using control vector Lyapunov functions, we present a universal decentralized feedback stabilizer for a decentralized affine in the control nonlinear impulsive dynamical system. These results are then used to develop decentralized controllers for large-scale impulsive dynamical systems with robustness guarantees against full modeling uncertainty.
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dc.title Control vector lyapunov functions for large-scale impulsive dynamical systems.
dc.creator Nersesov, Sergey.
Haddad, Wassim.
dc.description Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we provide generalizations to the recent extensions of vector Lyapunov theory for continuous-time systems to address stability and control design of impulsive dynamical systems via vector Lyapunov functions. Specifically, we provide a generalized comparison principle involving hybrid comparison dynamics that are dependent on comparison system states as well as the nonlinear impulsive dynamical system states. Furthermore, we develop stability results for impulsive dynamical systems that involve vector Lyapunov functions and hybrid comparison inequalities. Based on these results, we show that partial stability for state-dependent impulsive dynamical systems can be addressed via vector Lyapunov functions. Furthermore, we extend the novel notion of control vector Lyapunov functions to impulsive dynamical systems. Using control vector Lyapunov functions, we present a universal decentralized feedback stabilizer for a decentralized affine in the control nonlinear impulsive dynamical system. These results are then used to develop decentralized controllers for large-scale impulsive dynamical systems with robustness guarantees against full modeling uncertainty.
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dc.source Proceedings of the 45th IEEE Conference on Decision & Control, Manchester Grand Hyatt Hotel, San Diego, CA, USA, December 13-15, 2006, pg. 4813-4820.
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