Norm-controllability, or how a nonlinear system responds to large inputs

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Abstract

The purpose of this paper is to survey and discuss recent results on norm-controllability of nonlinear systems. This notion captures the responsiveness of a nonlinear system with respect to the applied inputs in terms of the norm of an output map, and can be regarded as a certain type of gain concept and/or a weaker notion of controllability. We state several Lyapunov-like sufficient conditions for this property in a simplified formulation, and illustrate the concept with several examples.

Keywords

Nonlinear Systems
Controllability
Lyapunov Methods
Input-to-State Stability

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* The work of the first and third author was supported by the German Research Foundation (DFG) within the Priority Programme 1305 “Control Theory of Digitally Networked Dynamical Systems” and within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart. The work of the second author was supported by the NSF grants CNS-1217811 and ECCS-1231196, and by a National Research Foundation Grant funded by the Korean Government (NRF-2011-220-D00043).

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