Remarks on universal nonsingular controls for discrete-time systems

Systems and Control Letters

Volumn 33, Issue 2, 1998, Pages 81-88

  Sontag, Eduardo D ^a   Wirth, Fabian R ^b  

^a RUTGERS UNIVERSITY   (United States)

^b UNIVERSITY OF BREMEN   (Germany)

Author keywords

Analytic discrete time systems; Forward accessibility; Universal controls

Indexed keywords

EID: 0002733495     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(97)00117-5     Document Type: Article

References (16)

1. F. Albertini, E.D. Sontag, Discrete-time transitivity and accessibility: analytic systems, SIAM J. Control Optim. 31 (6) (1993) 1599-1622.
2. F. Albertini, E.D. Sontag, Further results on controllability properties of discrete-time nonlinear systems, Dynamics and Control 4 (1994) 235-253.
3. M. Atiyah, I. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, MA, 1969.
4. J. Bochnak, M. Coste, M.-F. Roy, Géométrie algébrique réelle, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge Band 12, Springer, Berlin, 1987.
5. B. Jakubczyk, E.D. Sontag, Controllability of nonlinear discrete time systems: A Lie algebraic approach, SIAM J. Control Optim. 28 (1) (1990) 1-33.
6. L. Kaup, B. Kaup, Holomorphic Functions of Several Variables: An Introduction to the Fundamental Theory, Studies in Mathematics, vol. 3, de Gruyter, New York, 1983.
7. R. Narasimhan, Introduction to the Theory of Analytic Spaces, Lecture Notes in Mathematics, vol. 25, Springer, Berlin, 1966.
8. E.D. Sontag, On the observability of polynomial systems, I: Finite-time problems, SIAM J. Control Optim. 17 (1) (1979) 139-151.
9. E.D. Sontag, Universal nonsingular controls, System Control Lett. 19 (1992) 221-224; Errata, ibid. 20 (1993) 77.
10. E.D. Sontag, Critical points for least-squares problems involving certain analytic functions, with applications to sigmoidal nets, Adv. Comput. Math. (Special Issue on Neural Networks) 5 (1996) 245-268; Summary as "Critical points for neural net least-squares problems", in: Proc. 1995 IEEE Internat. Conf. Neural Networks, IEEE Publications, 1995, pp. 2949-2954.
11. E.D. Sontag, Critical points for least-squares problems involving certain analytic functions, with applications to sigmoidal nets, Adv. Comput. Math. (Special Issue on Neural Networks) 5 (1996) 245-268; Summary as "Critical points for neural net least-squares problems", in: Proc. 1995 IEEE Internat. Conf. Neural Networks, IEEE Publications, 1995, pp. 2949-2954.
12. E.D. Sontag, Y. Wang, Orders of input/output differential equations and state-space dimensions, SIAM J. Control Optim. 33 (4) (1995) 1102-1126.
13. H.J. Sussmann, Single-input observability of continuous-time systems, Math. Systems Theory 12 (1979) 371-393.
14. H.J. Sussmann, Real-analytic desingularization and subanalytic sets: an elementary approach, Trans. AMS 317 (2) (1990) 417-461.
15. F. Wirth, Universal controls for homogeneous discrete-time systems, Proc. 34th IEEE CDC, New Orleans, LA, 1995, pp. 25-26.
16. F. Wirth, Dynamics of time-varying discrete-time linear systems: spectral theory and the projected system, SIAM J. Control Optim. 36 (2) (1998), to appear.