1. 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.




2. E.D. Sontag. On quasireachable realizations of a polynomial response. In Systems analysis (Conf., Bordeaux, 1978), volume 75 of Astérisque, pages 207-217. Soc. Math. France, Paris, 1980.



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

   Necessary and sufficient conditions are given for a matrix over a ring to admit a Moore-Penrose generalized inverse in a weak sense. (Attached is also a Math Review with additional comments on strong inverses.)




4. E.D. Sontag. On the length of inputs necessary in order to identify a deterministic linear system. IEEE Trans. Automat. Control, 25(1):120-121, 1980. [PDF] Abstract:

   The family of m-input, n-dimensional linear systems can be globally Identified with a generic input sequence of length 2mn. This bound is the best possible. A best bound is proved also for a corresponding local identification problem.

1. E.D. Sontag. Nonlinear regulation, the piecewise linear approach. In Proc.Princeton Conf.on Information Sciences and Systems, Princeton, March 1980, 1980. Keyword(s): piecewise linear systems.



2. 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. [PDF] Keyword(s): feedback stabilization. Abstract:

   We show that, in general, it is impossible to stabilize a controllable system by means of a continuous feedback, even if memory is allowed. No optimality considerations are involved. All state spaces are Euclidean spaces, so no obstructions arising from the state space topology are involved either. For one dimensional state and input, we prove that continuous stabilization with memory is always possible. (This is an old conference paper, never published in journal form but widely cited nonetheless. Warning: file is very large, since it was scanned.)

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