1. 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. [PDF] Keyword(s): observability, zero-deficiency networks, systems biology, biochemical networks, observers, nonlinear stability, dynamical systems. Abstract:

   This paper provides a necessary and sufficient condition for detectability, and an explicit construction of observers when this condition is satisfied, for chemical reaction networks of the Feinberg-Horn-Jackson zero deficiency type.




2. E.D. Sontag and Y. Wang. Output-to-state stability and detectability of nonlinear systems. Systems Control Lett., 29(5):279-290, 1997. [PDF] [doi:http://dx.doi.org/10.1016/S0167-6911(97)90013-X] Keyword(s): input to state stability, detectability, input to state stability. Abstract:

   The notion of input-to-state stability (ISS) has proved to be useful in nonlinear systems analysis. This paper discusses a dual notion, output-to-state stability (OSS). A characterization is provided in terms of a dissipation inequality involving storage (Lyapunov) functions. Combining ISS and OSS there results the notion of input/output-to-state stability (IOSS), which is also studied and related to the notion of detectability, the existence of observers, and output injection.




3. M. L. J. Hautus and E.D. Sontag. An approach to detectability and observers. In Algebraic and geometric methods in linear systems theory (AMS-NASA-NATO Summer Sem., Harvard Univ., Cambridge, Mass., 1979), volume 18 of Lectures in Appl. Math., pages 99-135. Amer. Math. Soc., Providence, R.I., 1980. [PDF] Keyword(s): observability. Abstract:

   This paper proposes an approach to the problem of establishing the existence of observers for deterministic dynamical systems. This approach differs from the standard one based on Luenberger observers in that the observation error is not required to be Markovian given the past input and output data. A general abstract result is given, which special- izes to new results for parametrized families of linear systems, delay systems and other classes of systems. Related problems of feedback control and regulation are also studied.

1. M. Chaves and E.D. Sontag. An alternative observer for zero deficiency chemical networks. In Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001, pages 575-578, 2001. Keyword(s): observability, observers, zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems.



2. M. Chaves and E.D. Sontag. Observers for certain chemical reaction networks. In Proc. 2001 European Control Conf., Sep. 2001, pages 3715-3720, 2001. Keyword(s): zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems, observability, observers.

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