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Stability and Control of Large-Scale Dynamical SystemsA Vector Dissipative Systems Approach$
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Wassim M. Haddad and Sergey G. Nersesov

Print publication date: 2011

Print ISBN-13: 9780691153469

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153469.001.0001

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Control Vector Lyapunov Functions for Large-Scale Impulsive Systems

Control Vector Lyapunov Functions for Large-Scale Impulsive Systems

(p.271) Chapter Eleven Control Vector Lyapunov Functions for Large-Scale Impulsive Systems
Stability and Control of Large-Scale Dynamical Systems

Wassim M. Haddad

Sergey G. Nersesov

Princeton University Press

This chapter extends the notion of control vector Lyapunov functions to impulsive dynamical systems. Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In particular, the use of vector Lyapunov functions in dynamical system theory offers a very flexible framework since each component of the vector Lyapunov function can satisfy less rigid requirements as compared to a single scalar Lyapunov function. Using control vector Lyapunov functions, the chapter develops a universal hybrid decentralized feedback stabilizer for a decentralized affine in the control nonlinear impulsive dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel. These results are used to develop hybrid decentralized controllers for large-scale impulsive dynamical systems with robustness guarantees against full modeling and input uncertainty.

Keywords:   control vector Lyapunov function, impulsive dynamical system, vector Lyapunov function, feedback stabilizer, decentralized affine, gain margin, sector margin, hybrid decentralized controller

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