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
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
More details on these papers, and downloadable versions of almost all, are on my website
 E.D. Sontag. Monotone and near-monotone biochemical networks. Systems and
Synthetic Biology, 1:59–87, 2007.
 D. Del Vecchio, A.J. Ninfa, and E.D. Sontag. Modular cell biology: Retroactivity and
insulation. Nature Molecular Systems Biology, 4:161, 2008.
 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.
 E.D. Sontag. Network reconstruction based on steady-state data. Essays in
Biochemistry, 45, 2008. to appear.
 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.
 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.
 A. Maayan, R. Iyengar, and E.D. Sontag. Intracellular regulatory networks are close
to monotone systems. IET Systems Biology, to appear, 2008.
 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.
 A.M. Weinstein and E.D. Sontag. Modeling proximal tubule cell homeostasis: Tracking
changes in luminal flow. Bulletin of Mathematical Biology, 2008. Submitted.
 W. Maass, P. Joshi, and E.D. Sontag. Computational aspects of feedback in neural
circuits. PLoS Computational Biology, 3:e165 1–20, 2007.
 E.D. Sontag. Mathematical Control Theory. Deterministic Finite-Dimensional Systems,
volume 6 of Texts in Applied Mathematics. Springer-Verlag, New York, second edition,
 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.
 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.
 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.
 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
 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.
 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.
 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.
 E.D. Sontag. For differential equations with r parameters, 2r+1 experiments are enough
for identification. J. Nonlinear Sci., 12(6):553–583, 2002.
 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.
 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.
 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.
 L. Wang and E.D. Sontag. Singularly perturbed monotone systems and an application
to double phosphorylation cycles. J. Nonlinear Science, 2008.
 E.D. Sontag. Molecular systems biology and control. Eur. J. Control, 11(4-5):396–435,
 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.
 E.D. Sontag. Adaptation and regulation with signal detection implies internal model.
Systems Control Lett., 50(2):119–126, 2003.
 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.
 L. Moreau and E.D. Sontag. Balancing at the border of instability. Phys. Rev. E (3),
68(2):020901, 4, 2003.
 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.
 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.
 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.
 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.
 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.
 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,
 E.D. Sontag. Nonlinear regulation: the piecewise linear approach. IEEE Trans.
Automat. Control, 26(2):346–358, 1981.
 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.
 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,
 Y.S. Ledyaev and E.D. Sontag. A Lyapunov characterization of robust stabilization.
Nonlinear Anal., 37(7, Ser. A: Theory Methods):813–840, 1999.
 E.D. Sontag. Clocks and insensitivity to small measurement errors. ESAIM Control
Optim. Calc. Var., 4:537–557, 1999.
 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.
 E.D. Sontag. Vc dimension of neural networks. In C.M. Bishop, editor, Neural Networks
and Machine Learning, pages 69–95. Springer, Berlin, 1998.
 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.
 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.
 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.
 E.D. Sontag. Control of systems without drift via generic loops. IEEE Trans. Automat.
Control, 40(7):1210–1219, 1995.
 H. T. Siegelmann and E.D. Sontag. On the computational power of neural nets. J.
Comput. System Sci., 50(1):132–150, 1995.
 H. T. Siegelmann and E.D. Sontag. Analog computation via neural networks. Theoret.
Comput. Sci., 131(2):331–360, 1994.
 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.
 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,
 F. Albertini and E.D. Sontag. Further results on controllability properties of
discrete-time nonlinear systems. Dynam. Control, 4(3):235–253, 1994.
 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.
 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.
 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:
 E.D. Sontag. Feedback stabilization using two-hidden-layer nets. IEEE Trans. Neural
Networks, 3:981–990, 1992.
 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.
 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.
 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.
 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.
 E.D. Sontag. Linear systems over commutative rings: A survey. Ricerche di Automatica,
 E.D. Sontag. A characterization of asymptotic controllability. In Dynamical Systems
II, pages 645–648. Academic Press, NY, 1982.
 E.D. Sontag. A Lyapunov-like characterization of asymptotic controllability. SIAM J.
Control Optim., 21(3):462–471, 1983.
 E.D. Sontag. A “universal” construction of Artstein’s theorem on nonlinear
stabilization. Systems Control Lett., 13(2):117–123, 1989.
 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,
 E.D. Sontag. Controllability is harder to decide than accessibility. SIAM J. Control
Optim., 26(5):1106–1118, 1988.
 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
 E.D. Sontag. A remark on bilinear systems and moduli spaces of instantons. Systems
Control Lett., 9(5):361–367, 1987.
 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.
 B.W. Dickinson and E.D. Sontag. Dynamic realizations of sufficient sequences. IEEE
Trans. Inform. Theory, 31(5):670–676, 1985.
 C.A. Schwartz, B.W. Dickinson, and E.D. Sontag. Characterizing innovations
realizations for random processes. Stochastics, 11(3-4):159–172, 1984.
 E.D. Sontag. A concept of local observability. Systems Control Lett., 5(1):41–47, 1984.
 E.D. Sontag. Remarks on piecewise-linear algebra. Pacific J. Math., 98(1):183–201,
 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.
 E.D. Sontag. On generalized inverses of polynomial and other matrices. IEEE Trans.
Automat. Control, 25(3):514–517, 1980.
 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.
 E.D. Sontag. Polynomial Response Maps, volume 13 of Lecture Notes in Control and
Information Sciences. Springer-Verlag, Berlin, 1979.
 E.D. Sontag. Temas de Inteligencia Artificial. PROLAM, Buenos Aires, 1972.
 W. Dicks and E.D. Sontag. Sylvester domains. J. Pure Appl. Algebra, 13(3):243–275,