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arXiv · 1406.3224

Relaxed ISS Small-Gain Theorems for Discrete-Time Systems

Roman Geiselhart·Fabian R. Wirth
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Abstract

In this paper ISS small-gain theorems for discrete-time systems are stated, which do not require input-to-state stability (ISS) of each subsystem. This approach weakens conservatism in ISS small-gain theory, and for the class of exponentially ISS systems we are able to prove that the proposed relaxed small-gain theorems are non-conservative in a sense to be made precise. The proofs of the small-gain theorems rely on the construction of a dissipative finite-step ISS Lyapunov function which is introduced in this work. Furthermore, dissipative finite-step ISS Lyapunov functions, as relaxations of ISS Lyapunov functions, are shown to be sufficient and necessary to conclude ISS of the overall system.

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BibTeXRIS

Roman Geiselhart, Fabian R. Wirth. 2014-06-12. Relaxed ISS Small-Gain Theorems for Discrete-Time Systems. https://arxiv.org/abs/1406.3224

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