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

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Chapter Eight

Large-Scale Discrete-Time Interconnected Dynamical Systems

8.1 Introduction

Since most physical processes evolve naturally in continuous-time, it is not surprising that the bulk of large-scale dynamical system theory has been developed for continuous-time systems. Nevertheless, it is the overwhelming trend to implement controllers digitally. Hence, in this chapter we extend the notions of dissipativity theory [70, 170, 171] to develop vector dissipativity notions for large-scale nonlinear discrete-time dynamical systems. In particular, we introduce a generalized definition of dissipativity for large-scale nonlinear discrete-time dynamical systems in terms of a vector dissipation inequality involving a vector supply rate, a

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