Differential Inclusions, Control and Optimization 20 (2000) 51-62
doi: 10.7151/dmdico.1004

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A CONSTRUCTIVE METHOD FOR SOLVING STABILIZATION PROBLEMS

Vadim Azhmyakov

Institute of Mathematics and Computer Sciences
Ernst-Moritz-Arndt University of Greifswald
Jahnstr. 15a, D-17487 Greifswald, Germany
e-mail: azmjakow@mail.uni-greifswald.de

Abstract

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.

Keywords: differential inclusions, difference inclusions, Lyapunov function, asymptotic stability.

1991 Mathematics Subject Classification: 26E25, 93D05, 93D20.

References

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[7] A.P. Molchanov and Ye.S. Pyatnitskiy, Absolute instability of nonlinear nonstationary systems, Automation and Remote Control 43 (1982), 147-157.

Received 18 November 1999