1. E.D. Sontag. An approximation theorem in nonlinear sampling. In Mathematical theory of networks and systems (Beer Sheva, 1983), volume 58 of Lecture Notes in Control and Inform. Sci., pages 806-812. Springer, London, 1984. [PDF] Abstract:

   We continue here our investigation into the preservation of structural properties under the sampling of nonlinear systems. The main new result is that, under minimal hypothesis, a controllable system always satisfies a strong type of approximate sampled controllability.




2. C.A. Schwartz, B.W. Dickinson, and E.D. Sontag. Characterizing innovations realizations for random processes. Stochastics, 11(3-4):159-172, 1984. [PDF] Keyword(s): statistics, innovations, sufficient statistics. Abstract:

   In this paper we are concerned with the theory of second order (linear) innovations for discrete random processes. We show that of existence of a finite dimensional linear filter realizing the mapping from a discrete random process to its innovations is equivalent to a certain semiiseparable structure of the covariance sequence of the process. We also show that existence of a finite dimensional realization (linear or nonlinear) of the mapping from a process to its innovations implies that the process have this serniseparable covariance sequence property. In particular, for a stationary random process, the spectral density function must be rational.




3. E.D. Sontag. A concept of local observability. Systems Control Lett., 5(1):41-47, 1984. [PDF] Keyword(s): observability. Abstract:

   A notion of local observability, which is natural in the context of nonlinear input/output regulation. is introduced. A simple characterization is provided, a comparison is made with other local nonlinear observability definitions. and its behavior under constant-rate sampling is analyzed.




4. E.D. Sontag. An algebraic approach to bounded controllability of linear systems. Internat. J. Control, 39(1):181-188, 1984. [PDF] Keyword(s): saturation, bounded inputs. Abstract:

   In this note we present an algebraic approach to the proof that a linear system with matrices (A,B) is null-controllable using bounded inputs iff it is null-controllable (with unbounded inputs) and all eigenvalues of A have nonpositive real parts (continuous time) or magnitude not greater than one (discrete time). We also give the analogous results for the asymptotic case. Finally, we give an interpretation of these results in the context of local nonlinear controllability.




5. E.D. Sontag. Parametric stabilization is easy. Systems Control Lett., 4(4):181-188, 1984. [PDF] Keyword(s): systems over rings, systems over rings, parametric classes of systems. Abstract:

   A polynomially parametrized family of continuous-time controllable linear systems is always stabilizable by polynomially parametrized feedback.

1. E.D. Sontag. Remarks on input/output linearization. In Proc. IEEE Conf. Dec. and Control, Las Vegas, Dec. 1984, pages 409-412, 1984. [PDF] Abstract:

   In the context of realization theory, conditions are given for the possibility of simulating a given discrete time system, using immersion and/or feedback, by linear or state-affine systems.

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