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

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10.4 Extended Kalman-Yakubovich-Popov Conditions for Large-Scale Impulsive Dynamical Systems

In this section, we show that vector dissipativeness (respectively, exponential vector dissipativeness) of a large-scale impulsive dynamical system G of the form (10.54)–(10.57) can be characterized in terms of the local subsystem functions fci(·), Gci(·), hci(·), Jci(·), fdi(·), Gdi(·), hdi(·), and Jdi(·), along with the interconnection structures Ici(·) and Idi(·) for i = 1, …, q. For the results in this section we consider the special case of dissipative systems with quadratic vector hybrid supply rates and set D = Rn, Uci = Rmci, Udi = Rmdi, Yci = Rlci, and Ydi = Rldi. Furthermore, we assume that Z = Zx × Rmc, where Zx D, so that resetting occurs ...

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