12,045 research outputs found
Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems
Stabilization of non-stationary linear systems over noisy communication
channels is considered. Stochastically stable sources, and unstable but
noise-free or bounded-noise systems have been extensively studied in
information theory and control theory literature since 1970s, with a renewed
interest in the past decade. There have also been studies on non-causal and
causal coding of unstable/non-stationary linear Gaussian sources. In this
paper, tight necessary and sufficient conditions for stochastic stabilizability
of unstable (non-stationary) possibly multi-dimensional linear systems driven
by Gaussian noise over discrete channels (possibly with memory and feedback)
are presented. Stochastic stability notions include recurrence, asymptotic mean
stationarity and sample path ergodicity, and the existence of finite second
moments. Our constructive proof uses random-time state-dependent stochastic
drift criteria for stabilization of Markov chains. For asymptotic mean
stationarity (and thus sample path ergodicity), it is sufficient that the
capacity of a channel is (strictly) greater than the sum of the logarithms of
the unstable pole magnitudes for memoryless channels and a class of channels
with memory. This condition is also necessary under a mild technical condition.
Sufficient conditions for the existence of finite average second moments for
such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor
The Boundedness of Cauchy Integral Operator on a Domain Having Closed Analytic Boundary
In this paper, we prove that the Cauchy integral operators (or Cauchy
transforms) define continuous linear operators on the Smirnov classes for some
certain domain with closed analytic boundary
Tribonacci and Tribonacci-Lucas Sedenions
The sedenions form a 16-dimensional Cayley-Dickson algebra. In this paper, we
introduce the Tribonacci and Tribonacci-Lucas sedenions. Furthermore, we
present some properties of these sedenions and derive relationships between
them.Comment: 17 pages, 1 figur
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