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DCL Seminar: Matthew Philippe - Stability Analysis of Discrete-Time Linear Switching Systems with Graph-Constrained Switching Sequences

Event Type
Seminar/Symposium
Sponsor
Decision and Control Laboratory, Coordinated Science Laboratory
Location
CSL Auditorium, Room B02
Date
Feb 10, 2016   3:00 pm  
Speaker
Matthew Philippe, Ph.D. Student Université catholique de Louvain
Contact
Linda Meccoli
E-Mail
lmeccoli@illinois.edu
Phone
217-333-9449
Views
35
Originating Calendar
CSL Decision and Control Group

Decision and Control Lecture Series

Coordinated Science Laboratory

 

 “Stability Analysis of Discrete-Time Linear Switching Systems with Graph-Constrained Switching Sequences”

Matthew Philippe,

Ph.D. Student

Université catholique de Louvain
 

Wednesday, February 10, 2016

3:00 p.m. to 4:00 p.m.

CSL Auditorium (B02)

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“Stability Analysis of Discrete-Time Linear Switching Systems with Graph-Constrained Switching Sequences” 

Abstract:

Discrete-time linear switching systems are multi-modal dynamical systems that exhibit switching between a finite number of operating modes. They appear in both theoretical and practical applications, with examples including the study of networked control systems and biological systems.

We allow for the specification of rules on the possible sequences of mode in time, a.k.a. switching sequences, of the systems. For example, one may specify a maximum dwell time on a given mode, (a mode cannot be active more "X" times in a row), or more complex rules that may occur in practical settings. We use automata (edge-labeled graphs) to provide a concise representation of the accepted switching sequences.

We study the stability of these systems when the switching sequence is seen as a disturbance rather than a control input. Our main focus is on exponential stability. First, we present a new exact characterization of this property. Then, we present algorithms providing arbitrary accurate approximations of the exponential decay rate. These algorithms run with bounded computational complexity. We will also discuss the stability in a dead-beat sense, and present a polynomial-time algorithm for deciding this property.

Last, we will present a sufficient condition for the boundedness of all the trajectories of a system.

In each case, we will first discuss existing results in the context of arbitrary switching (when the switching is not subjected to any particular rules).

Then, we provide simple examples showing that these results cannot apply directly to our more general setting. Finally, we present answers for the constrained switching cases. 

Bio:

Matthew Philippe received his M.S. degree in Applied Mathematics Engineering in 2013 from the Université catholique de Louvain, Belgium. He is currently a Ph.D. student with Professor Raphaël Jungers in the Applied Mathematics department of the Institute of Information and Communication Technologies, Electronics and Applied Mathematics at the Université catholique de Louvain.

He received two awards (UCL-IEEE Student Branch - Best Master Thesis award, Alcatel-Lucent Bell MSc Thesis Awards 2013) for his master thesis "MPTCP Congestion control: Models and Design", and he was finalist of the "HSCC2015 - Best Student Paper Award" contest for the paper "A sufficient condition for the boundedness of matrix products accepted by an automaton".

His interests are the stability and performance analysis of hybrid and switching systems. 

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