A constructive method for solving stabilization problems

• Autorzy: Vadim Azhmyakov
• Języki publikacji: EN

Abstrakty

EN

The problem of asymptotic stabilization for a class of differential inclusions is considered. The problem of choosing the Lyapunov functions from the parametric class of polynomials for differential inclusions is reduced to that of searching saddle points of a suitable function. A numerical algorithm is used for this purpose. All the results thus obtained can be extended to cover the discrete systems described by difference inclusions.

Słowa kluczowe

EN

differential inclusions; difference inclusions; Lyapunov function; asymptotic stability

Kategorie tematyczne

• 93D05: Lyapunov and other classical stabilities (Lagrange, Poisson, L p , l p , etc.)
• 26E25: Set-valued functions
• 93D20: Asymptotic stability

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2000
• Tom: 20
• Numer: 1
• Strony: 51-62

Twórcy

autor

Vadim Azhmyakov

• Institute of Mathematics and Computer Sciences, Ernst-Moritz-Arndt University of Greifswald, Jahnstr. 15a, D-17487 Greifswald, Germany

Bibliografia

• [1] N.N. Krasovskii, Stability of Motion, Stanford University Press, Stanford, CA 1963.
• [2] A.F. Filippov, Stability for differential equations with discontinuous and many-valued right-hand sides, Differents. Uravn. 15 (1979), 1018-1027.
• [3] M. Kisielewicz, Differential Inclusions and Optimal Control, PWN-Kluver Acad. Publ., Dordrecht 1991.
• [4] V. Boltyanski, H. Martini and V. Soltan, Geometric Methods and Optimization Problems, Kluver Academic Publishers, Dordrecht 1999.
• [5] A.F. Filippov, Differential Equations with Discontinuous Right-Hand Side, Nauka, Moskow 1983. (in Russian)
• [6] J.P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin 1984.
• [7] A.P. Molchanov and Ye.S. Pyatnitskiy, Absolute instability of nonlinear nonstationary systems, Automation and Remote Control 43 (1982), 147-157.

Identyfikatory

DOI

10.7151/dmgt.1004