Ricardo Riaza

Departamento de Matemática Aplicada a las TIC

ETSI Telecomunicación, Universidad Politécnica de Madrid


ricardo.riaza(at)upm.es

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Differential-algebraic equations (DAEs)

DAEs are a class of implicit ordinary differential equations which arise as a modelling framework to describe a variety of systems in electrical engineering, mechanics, control theory, etc. They pose interesting mathematical problems from both an analytical and a numerical point of view.


You can find a freely available introduction to DAE theory in Chapter 1 of my book Differential-Algebraic Systems, World Scientific, 2008. The book presents several index notions and different approaches to the analysis of regular and singular DAEs, together with an introduction to DAE-based nonlinear circuit modelling.

 DAEs book

Some papers 

Find below a list of JCR papers that I have authored or co-authored on DAEs or on closely related topics. Papers on nonlinear circuit theory and memristors, which define the focus of much of my recent research, can be found here.

  • R. Riaza, Linearly implicit Liénard systems, Nonlinear Analysis A: Theory, Methods and Applications, Vol. 74 (2011) 213-223.

  • R. Riaza, Stability loss in quasilinear DAEs by divergence of a pencil eigenvalue, SIAM Journal on Mathematical Analysis, Vol. 41 (2010) 2226-2245.

  • R. März and R. Riaza, Linear differential-algebraic equations with properly stated-leading term: B-critical points, Dynamical Systems, Vol. 23 (2008) 505-522.

  • R. Riaza, Local dynamics of a family of quasilinear ODEs with folded singular equilibria, Nonlinear Analysis A: Theory, Methods and Applications, Vol. 68 (2008) 2242-2249.

  • R. Riaza and R. März, A simpler construction of the matrix chain defining the tractability index of linear DAEs, Applied Mathematics Letters, Vol. 21 (2008) 326-331.

  • R. März and R. Riaza, Linear differential-algebraic equations with properly stated-leading term: A-critical points, Mathematical and Computer Modelling of Dynamical Systems, Vol. 13 (2007) 291-314.

  • R. März and R. Riaza, Linear differential-algebraic equations with properly stated-leading term: Regular points, Journal of Mathematical Analysis and Applications, Vol. 323 (2006) 1279-1299.

  • W. Marszalek, T. Amdeberhan and R. Riaza, Singularity crossing phenomena in DAEs: a two-phase fluid flow application case study, Computers & Mathematics with Applications, Vol. 49 (2005) 303-319.

  • R. Riaza, Attraction domains of degenerate singular equilibria in quasi-linear ODEs, SIAM Journal on Mathematical Analysis, Vol. 36 (2004) 678-690.

  • R. Riaza and R. März, Linear index-1 DAEs: regular and singular problems, Acta Applicandae Mathematicae, Vol. 84 (2004) 29-53.

  • R. Riaza, Double SIB points in differential-algebraic systems, IEEE Transactions on Automatic Control, Vol. 48 (2003) 1625-1629.

  • R. Riaza, Stability issues in regular and non-critical singular DAEs, Acta Applicandae Mathematicae, Vol. 73 (2002) 301-336.

  • R. Riaza, On the Singularity-Induced Bifurcation Theorem, IEEE Transactions on Automatic Control, Vol. 47 (2002) 1520-1523.

  • R. Riaza, Singular bifurcations in higher index differential-algebraic equations, Dynamical Systems, Vol. 17 (2002) 243-261.

  • R. Riaza and P. J. Zufiria, Stability of singular equilibria in quasilinear implicit differential equations, Journal of Differential Equations, Vol. 171 (2001) 24-53.

  • R. Riaza, S. L. Campbell and W. Marszalek, On singular equilibria of index-1 DAEs, Circuits, Systems and Signal Processing, Vol. 19 (2000) 131-157.