Convergence of the solution set of singularly perturbed differential inclusions

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 8, 1997, Pages 5505-5514

  Veliov, Vladimir ^a,b  

^a UNIVERSITY OF VIENNA   (Austria)

^b INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

Author keywords

Control systems; Differential inclusion; Singular perturbation; Tikhonov's theorem

Indexed keywords

EID: 0043228273     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00413-6     Document Type: Article

References (15)

1. TIKHONOV A., Systems of differential equations containing a small parameter in the derivatives, Mat Sbornik, 31, 572-586 (1952). In Russian.
2. VASILIEVA A., On the development of singular perturbation theory at Moscow State University and elsewhere, SIAM Review, 36, 440-452 (1994).
3. KHALIL H., KOKOTOVIC P. & O'REILI J., Singular Perturbation Method in Control: Analysis and Design, Academic Press (1986).
4. DONTCHEV A. & SLAVOV I., Singular perturbation in a class of nonlinear differential inclusions, in System Modelling and Optimization (Edited by H.-.J. Sebastian and K. Tammer), Lecture Notes in Control and Inf. Sci., 143, pp. 273-280. Springer-Verlag, Berlin, Heidelberg, New York (1991).
5. DONTCHEV A., DONCHEV TZ. & SLAVOV I., On the upper semicontinuity of the set of solutions of differential inclusions with a small parameter in the derivative, IMA Preprint 1169, Institute for Mathematics and Its Applications, University of Minnesota (1993).
6. QUINCAMPOIX M., Singular perturbations for differential equations and inclusions: An approach through constrained systems, Report 9540, CEREMADE (URA CNRS 749) (1995).
7. VELIOV V., On the rigorous model simplification of control/uncertain systems with multiple time scales, Working Paper WP-96-82, International Institute for Applied Systems Analysis, Laxenburg, Austria (1996).
8. VELIOV V., Differential inclusions with stable subinclusions. Nonlinear Analysis, TMA, 23, 1027-1038 (1994).
9. QUINCAMPOIX M., Singular perturbations for systems of differential inclusions, in Geometry in Nonlinear Control and Differential Inclusions, pp. 341-348. Banach Center Publications, Warsaw (1995).
10. QUINCAMPOIX M., Singular perturbations in non-linear optimal control systems, Differential and Integral Equations, 8, 931-944 (1995).
11. DEIMLING K., Multivalued Differential Equations, Walter de Gruyter, Berlin, New York (1992).
12. CLARKE F., LEDYAEV Y., STERN R. & WOLENSKI P., Qualitative properties of trajectories of control systems: a survey, J. of Dynamical and Control Systems, 1, 1-48 (1995).
13. KRASTANOV M., Forward invariant sets, homogeneity and small-time controllability, in Geometry in Nonlinear Control and Differential Inclusions, pp. 287-300. Banach Center Publications, Warsaw (1995).
14. KOKOTOVIC P., Singular Perturbation Techniques in Control Theory, volume 90 of Lect. Notes in Control and Inf. Sci., pp. 1-50. Springer-Verlag, Berlin, Heidelberg, New York (1987).
15. BENSOUSSAN A., Perturbation Methods in Optimal Control Problems, Wiley, New York (1988).