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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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Large-Scale Impulsive Dynamical Systems

Large-Scale Impulsive Dynamical Systems

(p.211) Chapter Ten Large-Scale Impulsive Dynamical Systems
Stability and Control of Large-Scale Dynamical Systems

Wassim M. Haddad

Sergey G. Nersesov

Princeton University Press

This chapter develops vector dissipativity notions for large-scale nonlinear impulsive dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale nonlinear impulsive dynamical systems in terms of a hybrid vector dissipation inequality involving a vector hybrid supply rate, a vector storage function, and an essentially nonnegative, semistable dissipation matrix. The chapter also defines generalized notions of a vector available storage and a vector required supply and shows that they are element-by-element ordered, nonnegative, and finite. Extended Kalman-Yakubovich-Popov conditions, in terms of the local impulsive subsystem dynamics and the interconnection constraints, are developed for characterizing vector dissipativeness via vector storage functions for large-scale impulsive dynamical systems. Finally, using the concepts of vector dissipativity and vector storage functions as candidate vector Lyapunov functions, the chapter presents feedback interconnection stability results of large-scale impulsive nonlinear dynamical systems.

Keywords:   vector dissipativity, impulsive dynamical system, hybrid vector dissipation inequality, vector hybrid supply rate, vector storage function, semistable dissipation matrix, vector available storage, vector required supply, Kalman–Yakubovich–Popov conditions, vector Lyapunov function

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