598 research outputs found
Minimal positive realizations of transfer functions with nonnegative multiple poles
This note concerns a particular case of the minimality problem in positive system theory. A standard result in linear system theory states that any nth-order rational transfer function of a discrete time-invariant linear single-input-single-output (SISO) system admits a realization of order n. In some applications, however, one is restricted to realizations with nonnegative entries (i.e., a positive system), and it is known that this restriction may force the order N of realizations to be strictly larger than n. A general solution to the minimality problem (i.e., determining the smallest possible value of N) is not known. In this note, we consider the case of transfer functions with nonnegative multiple poles, and give sufficient conditions for the existence of positive realizations of order N = n. With the help of our results we also give an improvement of an existing result in positive system theory
Algorithm for positive realization of transfer functions
The aim of this brief is to present a finite-step algorithm for the positive realization of a rational
transfer function H(z). In comparision with previously described algorithms we emphasize that we do
not make an a priori assumption on (but, instead, include a finite step procedure for checking) the non-
negativity of the impulse response sequence of H(z). For primitive transfer functions a new method for
reducing the pole order of the dominant pole is also proposed
A lowerbound on the dimension of positive realizations
A basic phenomenon in positive system theory is that the dimension N of an arbitrary positive
realization of a given transfer function H(z) may be strictly larger than the dimension n of its minimal
realizations. The aim of this brief is to provide a non-trivial lower bound on the value of N under the
assumption that there exists a time instant k0 at which the (always nonnegative) impulse response of
H(z) is 0 but the impulse response becomes strictly positive for all k > k0. Transfer functions with this
property may be regarded as extremal cases in positive system theory
Order bound for the realization of a combination of positive filters
In a problem on the realization of digital ÂŻlters, initiated by Gersho and Gopinath [8], we extend and
complete a remarkable result of Benvenuti, Farina and Anderson [4] on decomposing the transfer function
t(z) of an arbitrary linear, asymptotically stable, discrete, time-invariant SISO system as a diÂźerence
t(z) = t1(z) ÂĄ t2(z) of two positive, asymptotically stable linear systems. We give an easy-to-compute
algorithm to handle the general problem, in particular, also the case of transfer functions t(z) with multiple
poles, which was left open in [4]. One of the appearing positive, asymptotically stable systems is always
1-dimensional, while the other has dimension depending on the order and, in the case of nonreal poles,
also on the location of the poles of t(z). The appearing dimension is seen to be minimal in some cases
and it can always be calculated before carrying out the realization
Positive decomposition of transfer functions with multiple poles
We present new results on decomposing the transfer function t(z) of a linear, asymptotically stable, discrete-time SISO system as a difference t(z) = t(1)(z) - t(2)(z) of two positive linear systems. We extend the results of [4] to a class of transfer functions t(z) with multiple poles. One of the appearing positive systems is always 1-dimensional, while the other has dimension corresponding to the location and order of the poles of t(z). Recently, in [11], a universal approach was found, providing a decomposition for any asymptotically stable t(z). Our approach here gives lower dimensions than [11] in certain cases but, unfortunately, at present it can only be applied to a relatively small class of transfer functions, and it does not yield a general algorithm
Archaeological geophysical surveys along the Pannonian Limes between 2015â2017
In the article the authors present the results of the magnetometry survey campaign supporting the World Heritage nomination of the Hungarian section of the âFrontiers of the Roman Empire â The Danube Limesâ between 2015 and 2017. During this task 116 hectares had been surveyed with geophysical methods alongside the Danube on elements of the Roman limes. Most of the features surveyed were temporary camps, watchtowers, settlements and the limes road itself on 65 archaeological sites. Even though more than 110 hectares had been surveyed, we are only scratching the surface of this enormous site complex. As the limes is comprehensible only at landscape-level, the opportunity to make large-scale surveys is very important. The opportunity to collect relevant data on that scale is crucial for research, so further surveys are needed
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