The input-to-state stability framework for multistable systems on manifolds

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Title: The input-to-state stability framework for multistable systems on manifolds
Authors: Forni, Paolo
Item Type: Thesis or dissertation
Abstract: As central topics in systems and control theory, the study of stability, robustness, and sensitivity to disturbances for nonlinear systems has gained with the Input-to-State Stability (ISS) paradigm one of its most powerful tools. Standard formulations of ISS and several related notions characterize stability properties in a global setting with respect to a single equilibrium in the origin and for systems defined in Euclidean space. This classical requirements make the basic theory not applicable for a global analysis of many dynamical behaviours of interest for applications, such as: multistability, periodic oscillations, and different class of attractors. The aim of this work is to extend and further characterize the variety of notions available in standard ISS literature to multistable systems evolving on Riemannian manifolds. The definition of global multistability in consideration is based on the existence of a finite number of compact, globally attractive, invariant sets satisfying a specific condition of acyclicity. Such definition allows for Lyapunov characterizations in hybrid systems and is used to generalize ISS, integral ISS, and Output-to-State Stability (OSS) to multistable systems on manifolds. In different modalities, the novel properties of ISS and integral ISS - respectively denoted as Input-to-State Multistability (ISM) and integral ISM - are shown to be preserved in cascade interconnection and with input shifts. In particular, under suitable conditions, we can establish semi-global practical ISM in perturbed flows and in singular perturbation models.
Content Version: Open Access
Issue Date: Aug-2017
Date Awarded: Mar-2018
Supervisor: Angeli, David
Department: Electrical and Electronic Engineering
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Electrical and Electronic Engineering PhD theses

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