  This doctoral thesis concerns novel distributed algorithms for weight
balancing over directed (communication) topologies. A directed topology
(digraph) with nonnegative (or positive) weights assigned on each edge is
weight-balanced if, for each node, the sum of the weights of in-coming edges
equals the sum of the weights of out-going edges. The novel algorithms
introduced in this thesis can facilitate the development of strategies for
generating weight balanced digraphs, in a distributed manner, and find numerous
applications in coordination and control of multi-component systems. In the
first part of this thesis, we introduce a novel distributed algorithm that
operates over a static topology and solves the weight balancing problem when
the weights are restricted to be nonnegative integers. In the second part of
the thesis, we present a novel distributed algorithm which solves the integer
weight balancing problem in the presence of arbitrary (time-varying and
inhomogeneous) delays that might affect the transmission at a particular link
at a particular time. In the third part of this thesis, we present a novel
distributed algorithm for obtaining admissible and balanced integer weights for
the case when there are lower and upper weight constraints on the communication
links. In the fourth part of this thesis we present a novel distributed
algorithm which solves the integer weight balancing problem under lower and
upper weight constraints over the communication links for the case where
arbitrary (time-varying and inhomogeneous) time delays and possible packet
drops affect the transmission at a particular link at a particular time.
