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Switched linear differential systems

Switched linear differential systems
Switched linear differential systems
In this thesis we study systems with switching dynamics and we propose new mathematical tools to analyse them. We show that the postulation of a global state space structure in current frameworks is restrictive and lead to potential difficulties that limit its use for the analysis of new emerging applications. In order to overcome such shortcomings, we reformulate the foundations in the study of switched systems by developing a trajectory-based approach, where we allow the use of models that are most suitable for the analysis of a each system. These models can involve sets of higher-order differential equations whose state space does not necessarily coincide.

Based on this new approach, we first study closed switched systems, and we provide sufficient conditions for stability based on LMIs using the concept of multiple higher order Lyapunov function. We also study the role of positive-realness in stability of bimodal systems and we introduce the concept of positive-real completion. Furthermore, we study open switched systems by developing a dissipativity theory. We give necessary and sufficient conditions for dissipativity in terms of LMIs constructed from the coefficient matrices of the differential equations describing the modes. The relationship between dissipativity and stability is also discussed.

Finally, we study the dynamics of energy distribution networks. We develop parsimonious models that deal effectively with the variant complexity of the network and the inherent switching phenomena induced by power converters. We also present the solution to instability problems caused by devices with negative impedance characteristics such as constant power loads, using tools developed in our framework.
Mayo Maldonado, Jonathan
67a88f33-f59e-46b2-abe6-386919d4f244
Mayo Maldonado, Jonathan
67a88f33-f59e-46b2-abe6-386919d4f244
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b

(2015) Switched linear differential systems. University of Southampton, Physical Sciences and Engineering, Doctoral Thesis, 133pp.

Record type: Thesis (Doctoral)

Abstract

In this thesis we study systems with switching dynamics and we propose new mathematical tools to analyse them. We show that the postulation of a global state space structure in current frameworks is restrictive and lead to potential difficulties that limit its use for the analysis of new emerging applications. In order to overcome such shortcomings, we reformulate the foundations in the study of switched systems by developing a trajectory-based approach, where we allow the use of models that are most suitable for the analysis of a each system. These models can involve sets of higher-order differential equations whose state space does not necessarily coincide.

Based on this new approach, we first study closed switched systems, and we provide sufficient conditions for stability based on LMIs using the concept of multiple higher order Lyapunov function. We also study the role of positive-realness in stability of bimodal systems and we introduce the concept of positive-real completion. Furthermore, we study open switched systems by developing a dissipativity theory. We give necessary and sufficient conditions for dissipativity in terms of LMIs constructed from the coefficient matrices of the differential equations describing the modes. The relationship between dissipativity and stability is also discussed.

Finally, we study the dynamics of energy distribution networks. We develop parsimonious models that deal effectively with the variant complexity of the network and the inherent switching phenomena induced by power converters. We also present the solution to instability problems caused by devices with negative impedance characteristics such as constant power loads, using tools developed in our framework.

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More information

Published date: June 2015
Organisations: University of Southampton, Vision, Learning and Control

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Local EPrints ID: 383678
URI: http://eprints.soton.ac.uk/id/eprint/383678
PURE UUID: a05d41d7-d2f9-4c78-8b6a-834851965e0a

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Date deposited: 11 Nov 2015 11:50
Last modified: 17 Jul 2017 20:11

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