135,890 research outputs found
Products of Generalized Stochastic Sarymsakov Matrices
In the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class
of stochastic Sarymsakov matrices is the largest known subset (i) that is
closed under matrix multiplication and (ii) the infinitely long left-product of
the elements from a compact subset converges to a rank-one matrix. In this
paper, we show that a larger subset with these two properties can be derived by
generalizing the standard definition for Sarymsakov matrices. The
generalization is achieved either by introducing an "SIA index", whose value is
one for Sarymsakov matrices, and then looking at those stochastic matrices with
larger SIA indices, or by considering matrices that are not even SIA. Besides
constructing a larger set, we give sufficient conditions for generalized
Sarymsakov matrices so that their products converge to rank-one matrices. The
new insight gained through studying generalized Sarymsakov matrices and their
products has led to a new understanding of the existing results on consensus
algorithms and will be helpful for the design of network coordination
algorithms
Secure and Private Implementation of Dynamic Controllers Using Semi-Homomorphic Encryption
This paper presents a secure and private implementation of linear
time-invariant dynamic controllers using Paillier's encryption, a
semi-homomorphic encryption method. To avoid overflow or underflow within the
encryption domain, the state of the controller is reset periodically. A control
design approach is presented to ensure stability and optimize performance of
the closed-loop system with encrypted controller.Comment: Improved numerical exampl
Vertex adjacencies in the set covering polyhedron
We describe the adjacency of vertices of the (unbounded version of the) set
covering polyhedron, in a similar way to the description given by Chvatal for
the stable set polytope. We find a sufficient condition for adjacency, and
characterize it with similar conditions in the case where the underlying matrix
is row circular. We apply our findings to show a new infinite family of
minimally nonideal matrices.Comment: Minor revision, 22 pages, 3 figure
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