Nonlinear small-gain theorems for input-to-state stability of infinite\n interconnections

2020/07/11 by Andrii Mironchenko, Mironchenko, Andrii, Christoph Kawan +3 · 2 citations
Materials Science · Engineering · Biochemistry, Genetics and Molecular Biology · #Magnetism in coordination complexes #Stability and Control of Uncertain Systems #Electron Spin Resonance Studies

paper · pdf · doi:10.48550/arxiv.2007.05705

Abstract

We consider infinite heterogeneous networks, consisting of input-to-state\nstable subsystems of possibly infinite dimension. We show that the network is\ninput-to-state stable, provided that the gain operator satisfies a certain\nsmall-gain condition. We show that for finite networks of nonlinear systems\nthis condition is equivalent to the so-called strong small-gain condition of\nthe gain operator (and thus our results extend available results for finite\nnetworks), and for infinite networks with a linear gain operator they\ncorrespond to the condition that the spectral radius of the gain operator is\nless than one. We provide efficient criteria for input-to-state stability of\ninfinite networks with linear gains, governed by linear and homogeneous gain\noperators, respectively.\n

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• A Lyapunov-Based Small-Gain Theorem for Fixed-Time ISS: Theory, Optimization, and Games
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