### Abstract

In the qualitative theory of non-linear networks the non-linear n-ports are generally considered either locally passive or globally passive even eventually globally passive (the most restrictive or the least restrictive properties respectively). Moreover the reciprocity condition in many cases (e. g. complete stability) restricts the area of applications. In the area of economics and other fields, basically motivated by Sandberg's results, the role of the off-diagonally monotone and antitone mapping is crucial. Based on the above facts and results, it is shown that partly similar classes of mappings could have a role in non-linear network theory. More precisely, the off-diagonally locally active (passive) n-ports, defined in the paper, could represent an important new class of n-ports. As an application of the features of this new class of n-ports two Theorems are given showing conditions under which in case of a network consisting of off-diagonally locally active n-ports the DC solution can be uniquely calculated using the standard iterative methods and an autonomous network is asymptotically stable in a given domain. Hence, this paper partially overcomes the so called 'curse of non-reciprocity'.

Original language | English |
---|---|

Pages (from-to) | 393-399 |

Number of pages | 7 |

Journal | International Journal of Circuit Theory and Applications |

Volume | 9 |

Issue number | 4 |

Publication status | Published - Oct 1981 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

**POSSIBILITY OF FILLING THE GAP BETWEEN LOCAL AND GLOBAL PASSIVITY OF NON-LINEAR NETWORKS AND SOME OF ITS CONSEQUENCES.** / Roska, T.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - POSSIBILITY OF FILLING THE GAP BETWEEN LOCAL AND GLOBAL PASSIVITY OF NON-LINEAR NETWORKS AND SOME OF ITS CONSEQUENCES.

AU - Roska, T.

PY - 1981/10

Y1 - 1981/10

N2 - In the qualitative theory of non-linear networks the non-linear n-ports are generally considered either locally passive or globally passive even eventually globally passive (the most restrictive or the least restrictive properties respectively). Moreover the reciprocity condition in many cases (e. g. complete stability) restricts the area of applications. In the area of economics and other fields, basically motivated by Sandberg's results, the role of the off-diagonally monotone and antitone mapping is crucial. Based on the above facts and results, it is shown that partly similar classes of mappings could have a role in non-linear network theory. More precisely, the off-diagonally locally active (passive) n-ports, defined in the paper, could represent an important new class of n-ports. As an application of the features of this new class of n-ports two Theorems are given showing conditions under which in case of a network consisting of off-diagonally locally active n-ports the DC solution can be uniquely calculated using the standard iterative methods and an autonomous network is asymptotically stable in a given domain. Hence, this paper partially overcomes the so called 'curse of non-reciprocity'.

AB - In the qualitative theory of non-linear networks the non-linear n-ports are generally considered either locally passive or globally passive even eventually globally passive (the most restrictive or the least restrictive properties respectively). Moreover the reciprocity condition in many cases (e. g. complete stability) restricts the area of applications. In the area of economics and other fields, basically motivated by Sandberg's results, the role of the off-diagonally monotone and antitone mapping is crucial. Based on the above facts and results, it is shown that partly similar classes of mappings could have a role in non-linear network theory. More precisely, the off-diagonally locally active (passive) n-ports, defined in the paper, could represent an important new class of n-ports. As an application of the features of this new class of n-ports two Theorems are given showing conditions under which in case of a network consisting of off-diagonally locally active n-ports the DC solution can be uniquely calculated using the standard iterative methods and an autonomous network is asymptotically stable in a given domain. Hence, this paper partially overcomes the so called 'curse of non-reciprocity'.

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M3 - Article

VL - 9

SP - 393

EP - 399

JO - International Journal of Circuit Theory and Applications

JF - International Journal of Circuit Theory and Applications

SN - 0098-9886

IS - 4

ER -