IJPAM: Volume 89, No. 5 (2013)

LYAPUNOV CONVERGENCE ANALYSIS FOR ASYMPTOTIC
TRACKING USING FORWARD AND BACKWARD
EULER APPROXIMATION OF DISCRETE
DIFFERENTIAL EQUATIONS

Paolo Mercorelli
Institute of Product and Process Innovation
Leuphana University of Lueneburg
Volgershall 1, D-21339 Lueneburg, GERMANY


Abstract. This paper proposes an analysis of the convergence of discrete differential equations obtained by Euler approximation methods. Backward and Feed-forward Euler approximations are considered. These kinds of methods are very often used in discretisation of continuous models because of their straightforward structure which allows an easy implementation in microprocessor applications. These two kinds of discretisations are very important in the representation of controllers in which the use of a fast algorithm of its discrete representation is a basic condition for the whole stability of the closed loop control structure.

Received: December 2, 2013

AMS Subject Classification: 93D20, 37B25, 49M25

Key Words and Phrases: asymptotic stability, Lyapunov functions and stability, discrete approximations

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DOI: 10.12732/ijpam.v89i5.11 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 5