A contraction-theory separation principle yields global exponential stability for controller-observer pairs and sharp LMI certificates for contractive RNNs, enabling stable output tracking and implicit neural network design.
Small-gain analysis of exponential incremental input/output-to-state stability for large-scale distributed systems
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abstract
We provide a detectability analysis for nonlinear large-scale distributed systems in the sense of exponential incremental input/output-to-state stability (i-IOSS). In particular, we prove that the overall system is exponentially i-IOSS if each subsystem is i-IOSS, with interconnections treated as external inputs, and a suitable small-gain condition holds. The analysis is extended to a Lyapunov characterization, resulting in a different quantitative outcome regarding the small-gain condition, which is further analyzed within this work. Moreover, we derive linear matrix inequality conditions posed solely on the local subsystems and their interconnections, which guarantee exponential i-IOSS of the overall distributed system. The results are illustrated on a numerical example.
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A Nonlinear Separation Principle via Contraction Theory: Applications to Neural Networks, Control, and Learning
A contraction-theory separation principle yields global exponential stability for controller-observer pairs and sharp LMI certificates for contractive RNNs, enabling stable output tracking and implicit neural network design.