1,721,060 research outputs found
Minimal positive realizations of transfer functions with real poles
No full textA standard result of linear-system theory states that a single-input-single-output (SISO) rational nth-order transfer function always has a state-space realization of the same order. In some applications, one is interested in having a realization with nonnegative entries (i.e., a positive system) and it is known that such constraints may lead to a minimal order positive realization of order much greater than the transfer function order. In this technical note, necessary and sufficient conditions for a third-order transfer function with distinct real poles to have a third-order positive realization are given: these conditions are expressed in terms of lower bounds for the first three samples of the impulse response and therefore are very easy to check. This result is an extension of a previous result for transfer functions with distinct real positive poles
A note on eigenvalues location for trace zero doubly stochastic matrices
Full text linkSome results on the location of the eigenvalues of trace zero doubly stochastic matrices are provided. A result similar to that provided in [H. Perfect and L. Mirsky. Spectral properties of doubly–stochastic matrices. Monatshefte f ̈ur Mathematik, 69(1):35–57, 1965.] for doubly stochastic matrices is given
An upper bound on the dimension of minimal positive realizations for discrete time systems
No full textIn some applications one is interested in having a state–space realization with nonnegative matrices (positive realization) of a given transfer function and it is known that such a realization may have a dimension strictly larger than the order of the transfer function itself. Moreover, in most cases, it is desirable to have a realization with minimal dimension. Unfortunately, it is not known, to date, how
to determine in general the minimum dimension of a positive realization and only lower and upper bounds to it are available. This letter provides an upper bound on the dimension of a minimal positive realization for transfer functions with simple poles. This is a considerable improvement on an earlier upper bound in which only transfer functions with real poles were considered
The NIEP and the positive realization problem
Full text linkThe nonnegative inverse eigenvalue problem is the problem of determining necessary and sufficient conditions for a multiset of complex numbers to be the spectrum of a nonnegative real matrix of size equal to the cardinality of the multiset itself. The problem is longstanding and proved to be very difficult so that several variations have been defined by considering particular classes of multisets and nonnegative real matrices. In this paper, a novel variation of the problem is proposed. This variation is motivated by a practical application in the positive realization problem, that is the problem of characterizing existence and minimality of a positive state–space representation of a given transfer function
A geometrical representation of the spectra of four dimensional nonnegative matrices
No full textA geometrical representation of the set of four complex numbers which are the spectrum of 4-dimensional entrywise nonnegative real matrices is provided. The characterization is based on the result for the nonnegative inverse eigenvalue problem (NIEP) from the coefficients of the characteristic polynomial given in [16]
On the reachable set for third-order linear discrete-time systems with positive control: The case of complex eigenvalues
No full textIn this paper, we study the geometrical properties of the set of reachable states of a single input third-order discrete-time linear system with positive controls. This set is a cone and we give a complete geometrical characterization of this set when the system has a complex conjugate pair of eigenvalues. More in detail, we give necessary and sufficient conditions for properness and polyhedrality of the cone and provide the number of its edges in terms of eigenvalue locations
The NIEP for four dimensional Leslie and doubly stochastic matrices with zero trace from the coefficients of the characteristic polynomial
Full text linkThe constraints on the coefficients of the characteristic polynomials of four dimensional doubly stochastic matrices with zero trace and Leslie stochastic matrices with zero trace are determined. Then, on the basis of these constraints, the regions of the complex plane consisting of those points which can serve as characteristic roots of four dimensional doubly stochastic matrices with zero trace and Leslie stochastic matrices with zero trace are characterized
On the reachable set for third-order linear discrete-time systems with positive control
No full textIn this paper we study the geometrical properties of the set of reachable states of a single-input third-order discrete-time linear system with positive controls. This set is a cone and we give a complete geometrical characterization of this set when the system has all real eigenvalues. More in detail, we give necessary and sufficient conditions for properness and polyhedrality of the cone and provide the number of its edges in terms of eigenvalue locations. Moreover, we provide necessary and sufficient conditions for finite time reachability of every reachable state and characterize the minimum number of steps needed to reach every state in terms of eigenvalue locations
The geometry of the reachability set for linear discrete-time systems with positive controls
No full textIn this paper we study the geometrical properties of the set of reachable states of a single input discrete-time linear time invariant (LTI) system with positive controls. This set is a cone and it can be expressed as the direct sum of a linear subspace arid a proper cone. In order to give a complete geometrical characterization of the reachable set, we provide a formula to evaluate the dimension of the largest reachable subspace and necessary and sufficient conditions for polyhedrality of the proper cone in terms of eigenvalues location. © 2006 Society for Industrial and Applied Mathematics
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