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Stability and Control of Large-Scale Dynamical Systems by Sergey G. Nersesov, Wassim M. Haddad

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Chapter Three

Large-Scale Continuous-Time Interconnected Dynamical Systems

3.1 Introduction

In this chapter, we develop vector dissipativity notions for large-scale nonlinear dynamical systems, a notion not previously considered in the literature. In particular, we introduce a generalized definition of dissipativity for large-scale nonlinear dynamical systems in terms of a vector dissipation inequality involving a vector supply rate, a vector storage function, and an essentially nonnegative, semistable dissipation matrix. The vector dissipation inequality reflects the fact that some of the supplied generalized energy of the large-scale system is stored, and some is dissipated. The dissipated generalized energy is nonnegative and is given ...

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