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Stability of infinitely many interconnected systems

: Dashkovskiy, Sergey; Mironchenko, Andrii; Schmid, Jochen; Wirth, Fabian


IFAC-PapersOnLine 52 (2019), Nr.16, S.550-555
ISSN: 2405-8963
ISSN: 1474-6670
Deutsche Forschungsgemeinschaft DFG
DA 767/7-1
Deutsche Forschungsgemeinschaft DFG
WI 1458/13-1
Deutsche Forschungsgemeinschaft DFG
MI 1886/2-1
Fraunhofer ITWM ()

In this paper we consider countable couplings of finite-dimensional input-to-state stable systems. We consider the whole interconnection as an infinite-dimensional system on the ℓ∞ state space. We develop stability conditions of the small-gain type to guarantee that the whole system remains ISS and highlight the differences between finite and infinite couplings by means of examples. We show that using our methodology it is possible to study uniform global asymptotic stability of nonlinear spatially invariant systems by solving a finite number of nonlinear algebraic inequalities.