Ricardo Riaza

Departamento de Matemática Aplicada a las TIC

ETSI Telecomunicación, Universidad Politécnica de Madrid


ricardo.riaza(at)upm.es

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Nonlinear circuits

Time-domain models of nonlinear circuits are often set up using a differential-algebraic formalism. This avoids the need to perform a state-space reduction (often unfeasible in practice) before addressing whatever analytical aspects or doing numerical simulation. Many simulators set up the circuit equations in DAE form. In this context, differential-algebraic models are often referred to as semistate models. A detailed introduction to DAE-based circuit modelling can be found in Chapters 5 and 6 of my book Differential-Algebraic Systems, World Scientific, 2008. 

After 2008, a considerable amount of research on nonlinear circuit theory were directed to circuits with memristors and other related devices.

More recently (since 2017) I have been working on a formalism based on projective geometry for general circuit modelling. Some results in this direction can be found in the Homogeneous circuit models section below.

Papers 

Here is a list of papers on circuit modelling and analysis and their application in Electronics, or on related topics:

Homogeneous circuit models


  • R. Riaza, Circuit theory in projective space and homogeneous circuit models, IEEE Transactions on Circuits and Systems I, accepted, in press, 2018.

  • Memristors and memory-devices

  • R. Riaza, Transcritical bifurcation without parameters in memristive circuits, SIAM Journal on Applied Mathematics, Vol. 78 (2018) 395-417.

  • I. García de la Vega and R. Riaza, Saddle-node bifurcations in classical and memristive circuits, International Journal of Bifurcation and Chaos, Vol. 26 (2016) 1650064.

  • R. Riaza, Second order mem-circuits, International Journal of Circuit Theory and Applications, Vol. 43 (2015) 1719-1742.

  • R. Riaza, Comment: Is memristor a dynamic element?, Electronics Letters, Vol. 50 (2014) 1342 - 1344.

  • R. Riaza, First order mem-circuits: modeling, nonlinear oscillations and bifurcations, IEEE Transactions on Circuits and Systems - I, Vol. 60 (2013) 1570-1583. Pre-peer reviewed version (Arxiv).

  • R. Riaza, Manifolds of equilibria and bifurcations without parameters in memristive circuits, SIAM J. Applied Mathematics, Vol. 72 (2012) 877-896.

  • F. García-Redondo and R. Riaza, The tractability index of memristive circuits: branch-oriented and tree-based models, Mathematical Methods in the Applied Sciences, Vol. 35 (2012) 1659-1699.

  • R. Riaza, Dynamical properties of electrical circuits with fully nonlinear memristors (pre-peer reviewed version, Arxiv). Nonlinear Analysis: Real World Applications, Vol. 12 (2011) 3674-3686. Final version (journal website).

  • R. Riaza, Explicit ODE reduction of memristive systems, International Journal of Bifurcation and Chaos, Vol. 21 (2011) 917-930.

  • R. Riaza and C. Tischendorf, Semistate models of electrical circuits including memristors, International Journal of Circuit Theory and Applications, Vol. 39 (2011) 607-627. Final version (journal website).

  • R. Riaza, Nondegeneracy conditions for active memristive circuits, IEEE Transactions on Circuits and Systems - II, Vol. 57 (2010) 223-227.

  • Analytical aspects of nonlinear circuit theory

  • I. García de la Vega and R. Riaza, Index and solvability of uncoupled circuits: A characterization without restrictions on their passivity, topology or controlling structure, Journal of Circuits, Systems, and Computers, Vol. 23 (2014) 1450087 (31 pages).

  • R. Riaza, DAEs in circuit modelling: A survey, in A. Ilchmann, T. Reis (eds.), Surveys in Differential-Algebraic Equations I, pp. 97-136, DAE Forum, Springer, 2013.

  • I. García de la Vega and R. Riaza, Hybrid analysis of nonlinear circuits: DAE models with indices zero and one, Circuits, Systems, and Signal Processing, Vol. 32 (2013) 2065-2095.

  • R. Riaza and C. Tischendorf, Structural characterization of classical and memristive circuits with purely imaginary eigenvalues, International Journal of Circuit Theory and Applications, Vol. 41 (2013) 273-294.

  • R. Riaza and C. Tischendorf, The hyperbolicity problem in electrical circuit theory, Mathematical Methods in the Applied Sciences, Vol. 33 (2010) 2037-2049. Final version (journal website).

  • R. Riaza, Graph-theoretic characterization of bifurcation phenomena in electrical circuit dynamics, International Journal of Bifurcation and Chaos, Vol. 20 (2010) 451-465.

  • A. J. Encinas and R. Riaza, Tree-based characterization of low index circuit configurations without passivity restrictions, International Journal of Circuit Theory and Applications, Vol. 36 (2008) 135-160.

  • R. Riaza and C. Tischendorf, Qualitative features of matrix pencils and DAEs arising in circuit dynamics, Dynamical Systems, Vol. 22 (2007) 107-131.

  • R. Riaza, Time-domain properties of reactive dual circuits, International Journal of Circuit Theory and Applications, Vol. 34 (2006) 317-340.

  • R. Riaza, Singularity-induced bifurcations in lumped circuits, IEEE Transactions on Circuits and Systems - I, Vol. 52 (2005) 1442-1450.

  • R. Riaza and J. Torres-Ramírez, Nonlinear circuit modelling via nodal methods, International Journal of Circuit Theory and Applications, Vol. 33 (2005) 281-305.

  • R. Riaza, A matrix pencil approach to the local stability analysis of non-linear circuits, International Journal of Circuit Theory and Applications, Vol. 32 (2004) 23-46. 

  • Applications of digraph theory to circuit analysis

  • R. Riaza, Cyclic matrices of weighted digraphs, Discrete Applied Mathematics, Vol. 160 (2012) 280-290.

  • R. Riaza and A. J. Encinas, Augmented nodal matrices and normal trees, Discrete Applied Mathematics, Vol. 158 (2010) 44-61.