Semistate models of electrical circuits including memristors

International Journal of Circuit Theory and Applications

Volumn 39, Issue 6, 2011, Pages 607-627

  Riaza, Ricardo ^a   Tischendorf, Caren ^b  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b UNIVERSITY OF COLOGNE   (Germany)

Author keywords

differential algebraic equation; index; lumped circuit; memristor; nodal analysis; semistate model

Indexed keywords

DIFFERENTIAL ALGEBRAIC EQUATIONS; INDEX; LUMPED CIRCUIT; MEMRISTOR; NODAL ANALYSIS; SEMISTATE MODEL;

ALGEBRA; COMPUTER SIMULATION; LUMPED PARAMETER NETWORKS; MEMRISTORS; NONLINEAR EQUATIONS; PASSIVE FILTERS; RESISTORS; TOPOLOGY;

ELECTRIC NETWORK ANALYSIS;

EID: 79956123841     PISSN: 00989886     EISSN: 1097007X     Source Type: Journal    
DOI: 10.1002/cta.665     Document Type: Article

References (61)

1. Chua LO,. Memristor - the missing circuit element. IEEE Transactions on Circuit Theory 1971; 18: 507-519.
2. Strukov DB, Snider GS, Stewart DR, Williams RS,. The missing memristor found. Nature 2008; 453: 80-83. (Pubitemid 351630336)
3. 2 memristors. Electronic Letters 2009; 45: 377-379.
4. 0.8O/Pt devices for nonvolatile memory applications. Applied Physics Letters 2008; 93. 093501.
5. Snider GS,. Spike-timing-dependent learning in memristive nanodevices. Proceedings of the IEEE International Symposium on Nanoscale Architectures, Anaheim, CA, 2008; 85-92.
6. Wang X, Chen Y, Xi H, Li H, Dimitrov D,. Spintronic memristor through spin-torque-induced magnetization motion. IEEE Electron Device Letters 2009; 30: 294-297.
7. 2 memristor. Journal of the Electrochemical Society 2009; 156: 29-37.
8. Itoh M, Chua LO,. Memristor oscillators. International Journal of Bifurcation and Chaos 2008; 18: 3183-3206.
9. Encinas A, Riaza R,. Tree-based characterization of low index circuit configurations without passivity restrictions. International Journal of Circuit Theory and Applications 2008; 36: 135-160. (Pubitemid 351561235)
10. Reis T,. Circuit synthesis of passive descriptor systems - a modified nodal approach. International Journal of Circuit Theory and Applications 2010; 38 (in press).
11. Reiszig G,. Differential-algebraic equations and impasse points. IEEE Transactions on Circuits and Systems, Part I 1996; 43: 122-133.
12. Reiszig G,. The index of the standard circuit equations of passive RLCTG-networks does not exceed 2. Proceedings of the ISCAS'98, vol. 3, 1998; 419-422.
13. Riaza R,. Singularity-induced bifurcations in lumped circuits. IEEE Transactions Circuits and Systems I 2005; 52: 1442-1450. (Pubitemid 41078441)
14. Takamatsu M, Iwata S,. Index characterization of differential-algebraic equations in hybrid analysis for circuit simulation. International Journal of Circuit Theory and Applications 2010; 38 (in press).
15. Vlach J, Singhal K,. Computer Methods for Circuits Analysis and Design. Van Nostrand Reinhold ITP: New York, 1994.
16. Dziurla B, Newcomb R,. The Drazin inverse and semi-state equations. Proceedings of the International Symposium on Mathematical Theory of Networks and Systems, Delft, Netherlands, 1979; 283-289.
17. Newcomb RW,. The semistate description of nonlinear time-variable circuits. IEEE Transactions on Circuits and Systems 1981; 28: 62-71.
18. Estévez-Schwarz D, Tischendorf C,. Structural analysis of electric circuits and consequences for MNA. International Journal of Circuit Theory and Applications 2000; 28: 131-162. (Pubitemid 33034036)
19. Günther M, Feldmann U,. CAD-based electric-circuit modeling in industry, I: mathematical structure and index of network equations. Surveys on Mathematics for Industry 1999; 8: 97-129.
20. Günther M, Feldmann U,. CAD-based electric-circuit modeling in industry, II: impact of circuit configurations and parameters. Surveys on Mathematics for Industry 1999; 8: 131-157.
21. März R,. Differential algebraic systems with properly stated leading term and MNA equations. Modeling, Simulation, and Optimization of Integrated Circuits, Oberwolfach, 2001. International Series of Numerical Mathematics, vol. 146. Birkhäuser: Basel, 2003; 135-151.
22. Tischendorf C,. Topological index calculation of DAEs in circuit simulation. Surveys on Mathematics for Industry 1999; 8: 187-199.
23. Tischendorf C,. Coupled systems of differential algebraic and partial differential equations in circuit and device simulation. Modeling and numerical analysis. Habilitationsschrift, Humboldt-University, Berlin, 2003.
24. Brenan KE, Campbell SL, Petzold LR,. Numerical Solution of Initial-value Problems in Differential-Algebraic Equations. SIAM: Philadelphia, PA, 1996.
25. Griepentrog E, März R,. Differential-algebraic Equations and their Numerical Treatment, Teubner-Texte zur Mathematik, vol. 88. Teubner: Leipzig, 1986.
26. Hairer E, Wanner G,. Solving Ordinary Differential Equations II: Stiff and Differential-algebraic Problems. Springer: Berlin, 1996.
27. Kunkel P, Mehrmann V,. Differential-algebraic Equations. Analysis and Numerical Solution. EMS, 2006.
28. Rabier PJ, Rheinboldt WC,. Theoretical and numerical analysis of differential-algebraic equations. Handbook of Numerical Analysis, vol. VIII. North-Holland: Amsterdam, 2002; 183-540.
29. Riaza R,. Differential-algebraic Systems. Analytical Aspects and Circuit Applications. World Scientific: Singapore, 2008.
30. Gantmacher FR,. The Theory of Matrices, vols 1 and 2. Chelsea: New York, 1959.
31. Riaza R, Torres-Ramírez J,. Nonlinear circuit modeling via nodal methods. International Journal of Circuit Theory and Applications 2005; 33: 281-305. (Pubitemid 41068377)
32. Andrásfai B,. Graph Theory: Flows, Matrices. Adam Hilger: Bristol, 1991.
33. Bollobás B,. Modern Graph Theory. Springer: Berlin, 1998.
34. Chua LO, Desoer CA, Kuh ES,. Linear and Nonlinear Circuits. McGraw-Hill: New York, 1987.
35. Foulds LR,. Graph Theory Applications. Springer: Berlin, 1992.
36. Gear CW,. The simultaneous numerical solution of differential-algebraic equations. IEEE Transactions on Circuit Theory 1971; 18: 89-95.
37. Campbell SL,. Singular Systems of Differential Equations. Pitman: London, 1980.
38. Campbell SL,. Singular Systems of Differential Equations II. Pitman: London, 1982.
39. Lewis FL, (ed.). Special Issue on Semistate Systems. Circuits, Systems, and Signal Processing 1986; 5 (1).
40. Lewis FL, Mertzios VG, (eds). Special Issue on Recent Advances in Singular Systems. Circuits, Systems, and Signal Processing 1989; 8 (3).
41. Lewis FL, Campbell SL, Kociecki M, (eds). Special issue on implicit and robust systems. Circuits, Systems, and Signal Processing 1994; 13 (2-3).
42. Campbell SL,. A general form for solvable linear time varying singular systems of differential equations. SIAM Journal on Mathematical Analysis 1987; 18: 1101-1115.
43. Gear CW, Petzold LR,. Differential/algebraic systems and matrix pencils. In Matrix Pencils, Kagstrom B, Ruhe A, (eds), Lecture Notes in Mathematics, vol. 973. Springer: New York, 1983; 75-89.
44. Griepentrog E, März R,. Basic properties of some differential-algebraic equations. Zeitschrift für Analysis und ihre Anwendungen 1989; 8: 25-40.
45. Hairer E, Lubich C, Roche M,. The Numerical Solution of Differential-algebraic Systems by Runge-Kutta Methods. Lecture Notes in Mathematics, vol. 1409. Springer: New York, 1989.
46. Lewis FL,. A survey of linear singular systems. Circuits, Systems, and Signal Processing 1986; 5: 3-36.
47. Newcomb RW, Dziurla B,. Some circuits and systems applications of semistate theory. Circuits, Systems, and Signal Processing 1989; 8: 235-260.
48. Petzold LR,. Differential-algebraic equations are not ODEs. SIAM Journal on Scientific and Statistical Computing 1982; 3: 367-384.
49. Rheinboldt WC,. Differential-algebraic systems as differential equations on manifolds. Mathematics of Computation 1984; 43: 473-482.
50. Campbell SL, Gear CW,. The index of general nonlinear DAEs. Numerische Mathematik 1995; 72: 173-196. (Pubitemid 126006756)
51. Campbell SL, Griepentrog E,. Solvability of general differential algebraic equations. SIAM Journal on Scientific Computing 1995; 16: 257-270.
52. März R,. Numerical methods for differential algebraic equations. Acta Numerica 1992 1992: 141-198.
53. Rabier PJ, Rheinboldt WC,. A geometric treatment of implicit differential-algebraic equations. Journal of Differential Equations 1994; 109: 110-146.
54. Reich S,. On a geometrical interpretation of differential-algebraic equations. Circuits, Systems, and Signal Processing 1990; 9: 367-382.
55. Kunkel P, Mehrmann V,. Canonical forms for linear differential-algebraic equations with variable coefficients. Journal of Computational and Applied Mathematics 1994; 56: 225-251.
56. Kunkel P, Mehrmann V,. Local and global invariants of linear differential-algebraic equations and their relation. Electronic Transactions on Numerical Analysis 1996; 4: 138-157. (Pubitemid 38921283)
57. Traversa FL, Bonani F, Guerrieri SD,. A frequencydomain approach to the analysis of stability and bifurcations in nonlinear systems described by differential-algebraic equations. International Journal of Circuit Theory and Applications 2008; 36: 421-439.
58. März R,. Differential algebraic equations anew. Applied Numerical Mathematics 2002; 42: 315-335.
59. März R,. The index of linear differential algebraic equations with properly stated leading terms. Results in Mathematics 2002; 42: 308-338. (Pubitemid 36002927)
60. März R,. Solvability of linear differential algebraic equations with properly stated leading terms. Results in Mathematics 2004; 45: 88-105. (Pubitemid 38587136)
61. Horn RA, Johnson ChR,. Matrix Analysis. Cambridge University Press: Cambridge, 1985.