Nonnegative realizations of matrix transfer functions

Förster, K.-H.; Nagy, B.

doi:10.1016/s0024-3795(00)00076-8

Cited by 17 publications

(7 citation statements)

References 13 publications

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“…A rational transfer functioñ( ) is primitive if the maximum modulus pole of̃( ) is the only maximum real eigenvalue of ( + ), which is similar to concepts presented in discrete-time versions [5,20]. Thus, a transfer function ( ) is defined by a primitive transfer function, if̃( ) is a primitive transfer function for some .…”

Section: Lemma 3 Assume That̃( ) Is Decomposed Intõmentioning

confidence: 92%

A Constructive Positive Realization with Sparse Matrices for a Continuous-Time Positive Linear System

Kim

2013

Mathematical Problems in Engineering

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This paper discusses a computational method to construct positive realizations with sparse matrices for continuous-time positive linear systems with multiple complex poles. To construct a positive realization of a continuous-time system, we use a Markov sequence similar to the impulse response sequence that is used in the discrete-time case. The existence of the proposed positive realization can be analyzed with the concept of a polyhedral convex cone. We provide a constructive algorithm to compute positive realizations with sparse matrices of some positive systems under certain conditions. A sufficient condition for the existence of a positive realization, under which the proposed constructive algorithm works well, is analyzed.

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Section: Lemma 3 Assume That̃( ) Is Decomposed Intõmentioning

confidence: 92%

A Constructive Positive Realization with Sparse Matrices for a Continuous-Time Positive Linear System

Kim

2013

Mathematical Problems in Engineering

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“…Many advanced issues regarding positive system analysis and control have been studied by a large number of authors from the '70s. Just to cite a few: controllability [3][4][5][6], stabilization [7,8], behavioural approach [9,10], optimal control [11], identification [12], realization [5,[13][14][15][16][17][18] and switched systems [19].…”

Section: Introductionmentioning

confidence: 99%

Positive Dynamical Systems: New Applications, Old Problems

Benvenuti

Farina²

2023

Int. J. Control Autom. Syst.

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This review paper presents four relevant and very recent real-world application problems demanding developments of long-standing theoretical open problems in the field of positive systems research. Notably, the selected applications belong to very different fields of science and technology, ranging from biology and medicine to civil and electronic engineering. This clearly shows how pervasive positive systems are in mainstream research. Additionally, the theoretical issues stemming from these applications are the living proofs of how the apparently simple positivity constraint on the variables of interest makes the theory behind practical problems far from trivial, even for the linear case.

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“…These problems have been given considerable attention over the past decade. The existence problem was completely solved in [2] and [9], cf., [16,17,11], while a few particular cases of the minimality problem were settled in [8,13,19,3,23,22].…”

Section: Introductionmentioning

confidence: 99%

An efficient algorithm for positive realizations

Czaja¹,

Jaming²,

Matolcsi³

2008

Systems & Control Letters

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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

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Nonnegative realizations of matrix transfer functions

Cited by 17 publications

References 13 publications

A Constructive Positive Realization with Sparse Matrices for a Continuous-Time Positive Linear System

A Constructive Positive Realization with Sparse Matrices for a Continuous-Time Positive Linear System

Positive Dynamical Systems: New Applications, Old Problems

An efficient algorithm for positive realizations

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