A guide to some expository and otherwise most-relevant papers (Eduardo D. Sontag)

**(Note: very out of date - last updated Aug 2009)**

I am often asked to provide some pointers to the “main papers” on my website. This is very difficult to do, because there are too many different topics. The current page is one attempt.

Listed here are a subset of papers, picked according to one of two criteria: (1) expository/survey papers, and/or (2) main papers that are not referred-to in a paper of type (1). (For instance, a plurality of papers are on input to state stability and related matters; since there is a survey on ISS, no such papers are included).

Also, I generally tried not to include two papers of type (2) if one of them refers to the other.

More details on these papers, and downloadable versions of almost all, are on my website (http://www.math.rutgers.edu/ sontag/PUBDIR/index.html)

- Largely informal exposition of monotone systems: [1] pdf
- Modularity, insulation, and impedance in cell biology: [2] pdf
- p53 transcription binding site recognition: [3] pdf
- Reverse engineering using “Modular Response Analysis”: [4] pdfpdf
- Exposition of input to state stability and related concepts (with references to a very large number of papers in this website): [5] pdf
- Numerical-experimentation regarding systems “close to monotone”: [6] pdf [7] pdf
- Geometric aspects of parameter robustness: [8]
- Kidney modeling: [9]
- Simulation of neural microcircuits: [10] pdf
- Textbook in control theory: [11] pdf
- On-line (and updated often) lecture notes on Systems Biology and Biomath: pdf
- Some graph-theoretic questions in biological signal transduction networks: [12] pdf
- Circadian rhythms: [13] pdf
- Continuous vs Boolean synchronous and asynchronous models (Drosophila segment polarity): [14] pdf
- Passivity-based stability and secant condition: [15] pdf
- Universality theorem on identifiability of I/O systems; I/O representations: [16] pdf [17], pdf, [18] pdf
- Numbers of experiments for identifiability: [19] pdf
- Time-varying inputs suitable for identifiability (bilinear systems): [20] pdf
- Petri nets and dynamics of biochemical systems: [21] pdf
- Computing gains in some signaling networks: [22] pdf
- Singular perturbations of monotone systems: [23] pdf
- Very brief introduction to concepts in molecular biology: [24] pdf
- Internal model principle, adaptation, and integral control: [25] pdf, [26] pdf
- Learning theory and systems identification: [27] pdf
- Systems operating at criticality (bifurcation points): [28] pdf
- Global version of Filippov’s relaxation theorem: [29] pdf
- Optimal control of mechanical systems (robots, underwater vehicles): [30] pdf
- Minimum-phase nonlinear systems: [31] pdf
- Observers for certain chemical networks: [32] pdf
- Hybrid and piecewise-linear systems: [33] pdf, [34] pdf, [35] pdf
- Feinberg-Horn-Jackson theory: [36] pdf
- Discontinuous feedback: [37] pdf, [38] pdf, [39] pdf, [40] pdf
- Basic exposition of VC dimension: [41] pdf
- Chemostats with multiple nutrients: [42] pdf
- Recurrent neural networks: [43] pdf
- critical points in nonlinear least-squares problems [44] pdf
- Numerical approach to control of systems without drift: [45] pdf
- Computational power of neural nets, and “analog” computation: [46] pdf, [47] pdf
- ICM’94 paper on observables for nonlinear systems: [48] pdf
- Stabilization of linear systems with saturations: [49] pdf
- Controllability of discrete-time nonlinear systems: [50] pdf, [51] pdf
- Feedback stabilization exposition: [52] pdf
- Neural networks for feedback control: [53] pdf [54] pdf
- Approximation in non-Hilbert spaces [55] pdf
- Linear systems over rings: [56] pdf, [57] pdf, [58] pdf, [59] pdf
- Control-Lyapunov functions: [60] pdf, [61] pdf, [62] pdf
- Integrability of distributions on manifolds: [63] pdf
- Computational complexity of control-theory problems: [64] pdf, [65] pdf
- Moduli spaces of instantons: [66] pdf
- Image restoration and segmentation using annealing: [67] pdf
- Recursive computation of sufficient statistics; innovations: [68] pdf, [69] pdf
- Local observability of nonlinear systems: [70] pdf
- Piecewise-linear algebra: [71] pdf
- First paper on stable matrix fraction factorizations for multivariable systems: [72] pdf
- Matrix generalized inverses over rings: [73] pdf
- First paper on continuous-feedback stabilizability, obstructions and time-varying feedback: [74] pdf
- Algebraic-geometric approach to realization theory of discrete-time systems: [75] pdf
- Artificial intelligence (book in Spanish): [76] pdf
- Factorization-rank of matrices over rings: [77] pdf

[1] E.D. Sontag. Monotone and near-monotone biochemical networks. Systems and Synthetic Biology, 1:59–87, 2007.

[2] D. Del Vecchio, A.J. Ninfa, and E.D. Sontag. Modular cell biology: Retroactivity and insulation. Nature Molecular Systems Biology, 4:161, 2008.

[3] T. Riley, E.D. Sontag, P. Chen, and A. Levine. The transcriptional regulation of human p53-regulated genes. Nature Reviews Molecular Cell Biology, 9:402–412, 2008.

[4] E.D. Sontag. Network reconstruction based on steady-state data. Essays in Biochemistry, 45, 2008. to appear.

[5] E.D. Sontag. Input to state stability: Basic concepts and results. In P. Nistri and G. Stefani, editors, Nonlinear and Optimal Control Theory, pages 163–220. Springer-Verlag, Berlin, 2007.

[6] E.D. Sontag, A. Veliz-Cuba, R. Laubenbacher, and A.S. Jarrah. The effect of negative feedback loops on the dynamics of boolean networks. Biophysical Journal, 2008. To appear. Preprint in arXiv 0707.3468v1, 23 July 2007, DOI doi:10.1529/biophysj.107.125021.

[7] A. Maayan, R. Iyengar, and E.D. Sontag. Intracellular regulatory networks are close to monotone systems. IET Systems Biology, to appear, 2008.

[8] M. Chaves, A. Sengupta, and E.D. Sontag. Geometry and topology of parameter space: investigating measures of robustness in regulatory networks. J. of Mathematical Biology, 2008. Accepted subject to revisions. Preprint: arXiv:0710.4269, November 2007.

[9] A.M. Weinstein and E.D. Sontag. Modeling proximal tubule cell homeostasis: Tracking changes in luminal flow. Bulletin of Mathematical Biology, 2008. Submitted.

[10] W. Maass, P. Joshi, and E.D. Sontag. Computational aspects of feedback in neural circuits. PLoS Computational Biology, 3:e165 1–20, 2007.

[11] E.D. Sontag. Mathematical Control Theory. Deterministic Finite-Dimensional Systems, volume 6 of Texts in Applied Mathematics. Springer-Verlag, New York, second edition, 1998.

[12] R. Albert, B. DasGupta, R. Dondi, S. Kachalo, E.D. Sontag, A. Zelikovsky, and K. Westbrooks. A novel method for signal transduction network inference from indirect experimental evidence. Journal of Computational Biology, 14:927–949, 2007.

[13] D. Angeli and E.D. Sontag. Oscillations in i/o monotone systems. IEEE Transactions on Circuits and Systems, Special Issue on Systems Biology, 55:166–176, 2008. Preprint version in arXiv q-bio.QM/0701018, 14 Jan 2007.

[14] M. Chaves, E.D. Sontag, and R. Albert. Methods of robustness analysis for Boolean models of gene control networks. IET Systems Biology, 153:154–167, 2006.

[15] M. Arcak and E.D. Sontag. A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks. Mathematical Biosciences and Engineering, 5:1–19, 2008. Also, preprint: arxiv0705.3188v1 [q-bio], May 2007.

[16] E.D. Sontag and Y. Wang. Uniformly universal inputs. In Analysis and Design of Nonlinear Control Systems, volume 224, pages 9–24. Springer-Verlag, London, 2007.

[17] Y. Wang and E.D. Sontag. Orders of input/output differential equations and state-space dimensions. SIAM J. Control Optim., 33(4):1102–1126, 1995.

[18] Y. Wang and E.D. Sontag. Generating series and nonlinear systems: analytic aspects, local realizability, and i/o representations. Forum Math., 4(3):299–322, 1992.

[19] E.D. Sontag. For differential equations with r parameters, 2r+1 experiments are enough for identification. J. Nonlinear Sci., 12(6):553–583, 2002.

[20] E.D. Sontag, Y. Wang, and A. Megretski. Input classes for identification of bilinear systems. IEEE Transactions Autom. Control, to appear, 2008. Also arXiv math.OC/0610633, 20 Oct 2006, and short version in ACC’06.

[21] D. Angeli, P. de Leenheer, and E.D. Sontag. A Petri net approach to the study of persistence in chemical reaction networks. Mathematical Biosciences, 210:598–618, 2007. Preprint: arXiv q-bio.MN/068019v2, 10 Aug 2006.

[22] M. Chaves and E.D. Sontag. Exact computation of amplification for a class of nonlinear systems arising from cellular signaling pathways. Automatica, 42:1987–1992, 2006.

[23] L. Wang and E.D. Sontag. Singularly perturbed monotone systems and an application to double phosphorylation cycles. J. Nonlinear Science, 2008.

[24] E.D. Sontag. Molecular systems biology and control. Eur. J. Control, 11(4-5):396–435, 2005.

[25] B. Andrews, E.D. Sontag, and P. Iglesias. An approximate internal model principle: Applications to nonlinear models of biological systems. In Proc. 17th IFAC World Congress, Seoul, pages Paper FrB25.3, 6 pages, 2008. To appear.

[26] E.D. Sontag. Adaptation and regulation with signal detection implies internal model. Systems Control Lett., 50(2):119–126, 2003.

[27] P. Kuusela, D. Ocone, and E.D. Sontag. Learning complexity dimensions for a continuous-time control system. SIAM J. Control Optim., 43(3):872–898, 2004.

[28] L. Moreau and E.D. Sontag. Balancing at the border of instability. Phys. Rev. E (3), 68(2):020901, 4, 2003.

[29] B. Ingalls, E.D. Sontag, and Y. Wang. An infinite-time relaxation theorem for differential inclusions. Proc. Amer. Math. Soc., 131(2):487–499, 2003.

[30] M. Chyba, N. E. Leonard, and E.D. Sontag. Singular trajectories in multi-input time-optimal problems: Application to controlled mechanical systems. Journal of Dynamical and Control Systems, 9(1):103–129, 2003.

[31] D. Liberzon, A. S. Morse, and E.D. Sontag. Output-input stability and minimum-phase nonlinear systems. IEEE Trans. Automat. Control, 47(3):422–436, 2002.

[32] M. Chaves and E.D. Sontag. State-estimators for chemical reaction networks of Feinberg-Horn-Jackson zero deficiency type. European J. Control, 8:343–359, 2002.

[33] B. DasGupta and E.D. Sontag. A polynomial-time algorithm for checking equivalence under certain semiring congruences motivated by the state-space isomorphism problem for hybrid systems. Theor. Comput. Sci., 262(1-2):161–189, 2001.

[34] E.D. Sontag. Interconnected automata and linear systems: a theoretical framework in discrete-time. In Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control, pages 436–448. Springer-Verlag New York, Inc., Secaucus, NJ, USA, 1996.

[35] E.D. Sontag. Nonlinear regulation: the piecewise linear approach. IEEE Trans. Automat. Control, 26(2):346–358, 1981.

[36] E.D. Sontag. Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction. IEEE Trans. Automat. Control, 46(7):1028–1047, 2001.

[37] E.D. Sontag. Stability and stabilization: discontinuities and the effect of disturbances. In Nonlinear analysis, differential equations and control (Montreal, QC, 1998), volume 528 of NATO Sci. Ser. C Math. Phys. Sci., pages 551–598. Kluwer Acad. Publ., Dordrecht, 1999.

[38] Y.S. Ledyaev and E.D. Sontag. A Lyapunov characterization of robust stabilization. Nonlinear Anal., 37(7, Ser. A: Theory Methods):813–840, 1999.

[39] E.D. Sontag. Clocks and insensitivity to small measurement errors. ESAIM Control Optim. Calc. Var., 4:537–557, 1999.

[40] F. H. Clarke, Y.S. Ledyaev, E.D. Sontag, and A.I. Subbotin. Asymptotic controllability implies feedback stabilization. IEEE Trans. Automat. Control, 42(10):1394–1407, 1997.

[41] E.D. Sontag. Vc dimension of neural networks. In C.M. Bishop, editor, Neural Networks and Machine Learning, pages 69–95. Springer, Berlin, 1998.

[42] P. de Leenheer, S.A. Levin, E.D. Sontag, and C.A. Klausmeier. Global stability in a chemostat with multiple nutrients. J. Mathematical Biology, 52:419–438, 2006.

[43] E.D. Sontag. Recurrent neural networks: Some systems-theoretic aspects. In Dealing with Complexity: a Neural Network Approach, pages 1–12. Springer-Verlag, London, 1997.

[44] E.D. Sontag. Critical points for least-squares problems involving certain analytic functions, with applications to sigmoidal nets. Adv. Comput. Math., 5(2-3):245–268, 1996.

[45] E.D. Sontag. Control of systems without drift via generic loops. IEEE Trans. Automat. Control, 40(7):1210–1219, 1995.

[46] H. T. Siegelmann and E.D. Sontag. On the computational power of neural nets. J. Comput. System Sci., 50(1):132–150, 1995.

[47] H. T. Siegelmann and E.D. Sontag. Analog computation via neural networks. Theoret. Comput. Sci., 131(2):331–360, 1994.

[48] E.D. Sontag. Spaces of observables in nonlinear control. In Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), pages 1532–1545, Basel, 1995. Birkhäuser.

[49] H.J. Sussmann, E.D. Sontag, and Y. Yang. A general result on the stabilization of linear systems using bounded controls. IEEE Trans. Automat. Control, 39(12):2411–2425, 1994.

[50] F. Albertini and E.D. Sontag. Further results on controllability properties of discrete-time nonlinear systems. Dynam. Control, 4(3):235–253, 1994.

[51] B. Jakubczyk and E.D. Sontag. Controllability of nonlinear discrete-time systems: a Lie-algebraic approach. SIAM J. Control Optim., 28(1):1–33, 1990.

[52] E.D. Sontag. Feedback stabilization of nonlinear systems. In Robust control of linear systems and nonlinear control (Amsterdam, 1989), volume 4 of Progr. Systems Control Theory, pages 61–81. Birkhäuser Boston, Boston, MA, 1990.

[53] E.D. Sontag. Neural networks for control. In H. L. Trentelman and J. C. Willems, editors, Essays on control: perspectives in the theory and its applications (Groningen, 1993), volume 14 of Progr. Systems Control Theory, pages 339–380. Birkhäuser Boston, Boston, MA, 1993. A longer version (tech report with more details) is here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/neural-nets-siemens.pdf.

[54] E.D. Sontag. Feedback stabilization using two-hidden-layer nets. IEEE Trans. Neural Networks, 3:981–990, 1992.

[55] M. J. Donahue, L. Gurvits, C. Darken, and E.D. Sontag. Rates of convex approximation in non-Hilbert spaces. Constr. Approx., 13(2):187–220, 1997.

[56] E.D. Sontag and Y. Wang. Pole shifting for families of linear systems depending on at most three parameters. Linear Algebra Appl., 137/138:3–38, 1990.

[57] E.D. Sontag. An introduction to the stabilization problem for parametrized families of linear systems. In Linear algebra and its role in systems theory (Brunswick, Maine, 1984), volume 47 of Contemp. Math., pages 369–400. Amer. Math. Soc., Providence, RI, 1985.

[58] E.D. Sontag. Linear systems over commutative rings: a (partial) updated survey. In Control science and technology for the progress of society, Vol. 1 (Kyoto, 1981), pages 325–330. IFAC, Laxenburg, 1982.

[59] E.D. Sontag. Linear systems over commutative rings: A survey. Ricerche di Automatica, 7:1–34, 1976.

[60] E.D. Sontag. A characterization of asymptotic controllability. In Dynamical Systems II, pages 645–648. Academic Press, NY, 1982.

[61] E.D. Sontag. A Lyapunov-like characterization of asymptotic controllability. SIAM J. Control Optim., 21(3):462–471, 1983.

[62] E.D. Sontag. A “universal” construction of Artstein’s theorem on nonlinear stabilization. Systems Control Lett., 13(2):117–123, 1989.

[63] E.D. Sontag. Integrability of certain distributions associated with actions on manifolds and applications to control problems. In Nonlinear controllability and optimal control, volume 133 of Monogr. Textbooks Pure Appl. Math., pages 81–131. Dekker, New York, 1990.

[64] E.D. Sontag. Controllability is harder to decide than accessibility. SIAM J. Control Optim., 26(5):1106–1118, 1988.

[65] E.D. Sontag. From linear to nonlinear: some complexity comparisons. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995, pages 2916–2920, 1995.

[66] E.D. Sontag. A remark on bilinear systems and moduli spaces of instantons. Systems Control Lett., 9(5):361–367, 1987.

[67] E.D. Sontag and H.J. Sussmann. Image restoration and segmentation using the annealing algorithm. In Proc. IEEE Conf. Dec. and Control, 1985, pages 768–773, 1985.

[68] B.W. Dickinson and E.D. Sontag. Dynamic realizations of sufficient sequences. IEEE Trans. Inform. Theory, 31(5):670–676, 1985.

[69] C.A. Schwartz, B.W. Dickinson, and E.D. Sontag. Characterizing innovations realizations for random processes. Stochastics, 11(3-4):159–172, 1984.

[70] E.D. Sontag. A concept of local observability. Systems Control Lett., 5(1):41–47, 1984.

[71] E.D. Sontag. Remarks on piecewise-linear algebra. Pacific J. Math., 98(1):183–201, 1982.

[72] P.P. Khargonekar and E.D. Sontag. On the relation between stable matrix fraction factorizations and regulable realizations of linear systems over rings. IEEE Trans. Automat. Control, 27(3):627–638, 1982.

[73] E.D. Sontag. On generalized inverses of polynomial and other matrices. IEEE Trans. Automat. Control, 25(3):514–517, 1980.

[74] E.D. Sontag and H.J. Sussmann. Remarks on continuous feedback. In Proc. IEEE Conf. Decision and Control, Albuquerque, Dec.1980, pages 916–921, 1980.

[75] E.D. Sontag. Polynomial Response Maps, volume 13 of Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin, 1979.

[76] E.D. Sontag. Temas de Inteligencia Artificial. PROLAM, Buenos Aires, 1972.

[77] W. Dicks and E.D. Sontag. Sylvester domains. J. Pure Appl. Algebra, 13(3):243–275, 1978.