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Type of Document Dissertation Author Lorand, Cédric Author's Email Address clorand@hotmail.com URN etd-11012004-155915 Title A Theory of Synchronization Errors in Interconnected Systems Degree Master of Science in Electrical Engineering Department Electrical Engineering Advisory Committee
Advisor Name Title Panos J Antsaklis Committee Member Paulo Tabuada Committee Member Peter Heinz Bauer Committee Member Thomas E Fuja Committee Member Keywords
- Synchronization
- Networked
- Controlled Systems
Date of Defense 2004-09-24 Availability unrestricted Abstract The most important error-generating events in Network Control
Systems are known to be: time-variant communication delays, packet
drops, bandwidth limitations, and synchronization errors.
Synchronization errors constitute an important and often
overlooked network induced non-ideal behavior. Little is known
about their effects on system stability and performance
robustness. Therefore studying and understanding synchronization
errors is the primary objective of this thesis.
Most literature either assumes that all subsystems are working
synchronously or use a continuous-time model, to circumvent the
difficulties of the desynchronized discrete-time approach. Only a
few papers proposed a desynchronized discrete time model, using
certain idealized assumptions.
In this thesis we present two new models that efficiently capture
the salient effects of synchronization errors in interconnected
discrete-time systems: a state-space based model, and a system
description based on infinite dimensional Toeplitz like operators.
We first model and perform stability analysis for systems with
identical clock frequencies that are operating asynchronously.
This class of systems finds applications in high-speed circuitry.
The introduced stability analysis utilizes spectral methods, and a
proposed fault detection algorithm identifies desynchronized
sub-systems.
For the case of a two system control loop, it is shown that the
nature of the period ratio $frac{T_1}{T_2}$ profoundly affects
system behavior. The case of commensurate rates $frac{T_1}{T_2}$
is tackled using both, the state-space approach and the
infinite-dimensional operator approach. From the state-space
description it follows that the system is equivalent to a
periodic, time-variant, discrete-time system. Stability analysis
is then performed using the classical spectral techniques. The
Toeplitz based approach reveals an underlying periodic matrix
block pattern in the infinite-dimensional matrix representation.
This periodicity property is utilized to derive equivalent
stability conditions.
Finally, we investigate the case of irrational ratios
$frac{T_1}{T_2}$, using the two above-mentioned approaches. It is
shown that the infinite-dimensional matrix representation always
admits a sparse factorization. This amazing property will enable
the formulation of future stability conditions and computationally
efficient algorithms. Based on the state-space model, a sufficient
stability condition is derived, that can be made arbitrarily close
to being necessary at the expense of increased computations. The
case of period ratio uncertainties is also addressed.
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