15,009 research outputs found
Minimal positive realizations for a class of transfer functions
It is a standard result in linear-system theory that an nth-order rational transfer function of a single-input single-output system always 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. In this brief we present a class of transfer functions where positive realizations of order n do exist. With the help of our result we give improvements on some earlier results in positive-system theory
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
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
Finding complex balanced and detailed balanced realizations of chemical reaction networks
Reversibility, weak reversibility and deficiency, detailed and complex
balancing are generally not "encoded" in the kinetic differential equations but
they are realization properties that may imply local or even global asymptotic
stability of the underlying reaction kinetic system when further conditions are
also fulfilled. In this paper, efficient numerical procedures are given for
finding complex balanced or detailed balanced realizations of mass action type
chemical reaction networks or kinetic dynamical systems in the framework of
linear programming. The procedures are illustrated on numerical examples.Comment: submitted to J. Math. Che
An efficient algorithm for positive realizations
We observe that successive applications of known results from the theory of
positive systems lead to an {\it efficient general algorithm} for positive
realizations of transfer functions. We give two examples to illustrate the
algorithm, one of which complements an earlier result of \cite{large}. Finally,
we improve a lower-bound of \cite{mn2} to indicate that the algorithm is indeed
efficient in general
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
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
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