An ISS small gain theorem for general networks
TLDR
A generalized version of the nonlinear small gain theorem is provided for the case of more than two coupled input-to-state stable systems and an associated lower-dimensional discrete time dynamical system.Abstract:
We provide a generalized version of the nonlinear small gain theorem for the case of more than two coupled input-to-state stable systems. For this result the interconnection gains are described in a nonlinear gain matrix, and the small gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than 1. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated lower-dimensional discrete time dynamical system.read more
Citations
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Architectures for distributed and hierarchical Model Predictive Control - A review
TL;DR: A classification of a number of decentralized, distributed and hierarchical control architectures for large scale systems is proposed and attention is focused on the design approaches based on Model Predictive Control.
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Small Gain Theorems for Large Scale Systems and Construction of ISS Lyapunov Functions
TL;DR: In this paper, the authors consider interconnections of nonlinear subsystems in the input-to-state stability (ISS) framework, where a gain matrix is used to encode the mutual dependencies of the systems in the network.
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Input-to-State Stability of Nonlinear Impulsive Systems
TL;DR: It is proved that impulsive systems, which possess an input-to-state stable (ISS) Lyapunov function, are ISS for time sequences satisfying the fixed dwell-time condition and two small-gain theorems are proved that provide a construction of an ISS Lyap unov function for an interconnection of impulsive Systems if the ISS LyAPunov functions for subsystems are known.
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Distributed Moving Horizon Estimation for Linear Constrained Systems
TL;DR: Under weak observability conditions the authors prove convergence of the state estimates computed by any sensors to the correct state even when constraints on noise and state variables are taken into account in the estimation process.
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Plug-and-Play Decentralized Model Predictive Control for Linear Systems
TL;DR: This work considers a linear system structured into physically coupled subsystems and proposes a decentralized control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states and shows how to automatize the design of local controllers.
References
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Smooth stabilization implies coprime factorization
TL;DR: In this paper, it was shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system.