555,074 research outputs found
A Test for the Stability of Networks
A complex polynomial is called a Hurwitz polynomial, if all its roots have a real part smaller than zero. This kind of polynomial plays an all-dominant role in stability checks of electrical (analog or digital) networks. In this article we prove that a polynomial p can be shown to be Hurwitz by checking whether the rational function e(p)/o(p) can be realized as a reactance of one port, that is as an electrical impedance or admittance consisting of inductors and capacitors. Here e(p) and o(p) denote the even and the odd part of p [25].Rowinska-Schwarzweller Agnieszka - Chair of Display Technology University of Stuttgart Allmandring 3b, 70596 Stuttgart, GermanySchwarzweller Christoph - Institute of Computer Science University of Gdansk Wita Stwosza 57, 80-952 Gdansk, PolandGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990.Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.Anna Justyna Milewska. The field of complex numbers. Formalized Mathematics, 9(2): 265-269, 2001.Robert Milewski. The ring of polynomials. Formalized Mathematics, 9(2):339-346, 2001.Robert Milewski. The evaluation of polynomials. Formalized Mathematics, 9(2):391-395, 2001.Robert Milewski. Fundamental theorem of algebra. Formalized Mathematics, 9(3):461-470, 2001.Michał Muzalewski and Wojciech Skaba. From loops to abelian multiplicative groups with zero. Formalized Mathematics, 1(5):833-840, 1990.Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.Piotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Formalized Mathematics, 9(1):95-110, 2001.Christoph Schwarzweller. Introduction to rational functions. Formalized Mathematics, 20 (2):181-191, 2012. doi:10.2478/v10037-012-0021-1.Christoph Schwarzweller and Agnieszka Rowinska-Schwarzweller. Schur’s theorem on the stability of networks. Formalized Mathematics, 14(4):135-142, 2006. doi:10.2478/v10037-006-0017-9.Andrzej Trybulec and Czesław Bylinski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Rolf Unbehauen. Netzwerk- und Filtersynthese: Grundlagen und Anwendungen. Oldenbourg-Verlag, fourth edition, 1993.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992
A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks
This paper presents a stability test for a class of interconnected nonlinear
systems motivated by biochemical reaction networks. One of the main results
determines global asymptotic stability of the network from the diagonal
stability of a "dissipativity matrix" which incorporates information about the
passivity properties of the subsystems, the interconnection structure of the
network, and the signs of the interconnection terms. This stability test
encompasses the "secant criterion" for cyclic networks presented in our
previous paper, and extends it to a general interconnection structure
represented by a graph. A second main result allows one to accommodate state
products. This extension makes the new stability criterion applicable to a
broader class of models, even in the case of cyclic systems. The new stability
test is illustrated on a mitogen activated protein kinase (MAPK) cascade model,
and on a branched interconnection structure motivated by metabolic networks.
Finally, another result addresses the robustness of stability in the presence
of diffusion terms in a compartmental system made out of identical systems.Comment: See http://www.math.rutgers.edu/~sontag/PUBDIR/index.html for related
(p)reprint
A Test Bed for Evaluating the Performance of IoT Networks
The use of smaller, personal IoT networks has increased over the past several years. These devices demand a lot of resources but only have limited access. To establish and sustain a flexible network connection, 6LoWPAN with RPL protocol is commonly used. While RPL provides a low-cost solution for connection, it lacks load balancing mechanisms. Improvements in OF load balancing can be implemented to strengthen network stability. This paper proposes a test bed configuration to show the toll of frequent parent switching on 6LoWPAN. Contiki’s RPL 6LoWPAN software runs on STM32 Nucleo microcontrollers with expansion boards for this test bed. The configuration tests frequency of parent changes and packet loss to demonstrate network instability of different RPL OFs. Tests on MRHOF for RPL were executed to confirm the working configuration. Results, with troubleshooting and improvements, show a working bed. The laid-out configuration provides a means for testing network stability in IoT networks
Spatial patterns of desynchronization bursts in networks
We adapt a previous model and analysis method (the {\it master stability
function}), extensively used for studying the stability of the synchronous
state of networks of identical chaotic oscillators, to the case of oscillators
that are similar but not exactly identical. We find that bubbling induced
desynchronization bursts occur for some parameter values. These bursts have
spatial patterns, which can be predicted from the network connectivity matrix
and the unstable periodic orbits embedded in the attractor. We test the
analysis of bursts by comparison with numerical experiments. In the case that
no bursting occurs, we discuss the deviations from the exactly synchronous
state caused by the mismatch between oscillators
Recommended from our members
Distributed LQR design for identical dynamically coupled systems: Application to load frequency control of multi-area power grid
The paper proposes a distributed LQR method for the solution to regulator problems of networks composed of dynamically dependent agents. It is assumed that these dynamical couplings among agents can be expressed in a state-space form of a certain structure. Following a top-down approach we approximate a centralized LQR optimal controller by a distributed scheme the stability of which is guaranteed via a stability test applied to convex combination of Hurwitz matrices. The method is applied to N-identical-area power grid where a distributed state-feedback Load Frequency Controller (LFC) is proposed to achieve frequency regulation under power demand variations. An illustrative numerical example demonstrates the applicability of the method
Synchronization of dynamical hypernetworks: dimensionality reduction through simultaneous block-diagonalization of matrices
We present a general framework to study stability of the synchronous solution
for a hypernetwork of coupled dynamical systems. We are able to reduce the
dimensionality of the problem by using simultaneous block-diagonalization of
matrices. We obtain necessary and sufficient conditions for stability of the
synchronous solution in terms of a set of lower-dimensional problems and test
the predictions of our low-dimensional analysis through numerical simulations.
Under certain conditions, this technique may yield a substantial reduction of
the dimensionality of the problem. For example, for a class of dynamical
hypernetworks analyzed in the paper, we discover that arbitrarily large
networks can be reduced to a collection of subsystems of dimensionality no more
than 2. We apply our reduction techique to a number of different examples,
including a class of undirected unweighted hypermotifs of three nodes.Comment: 9 pages, 6 figures, accepted for publication in Phys. Rev.
- …