IJPAM: Volume 81, No. 5 (2012)

A DISCRETE APPROXIMATE SOLUTION FOR
THE ASYMPTOTIC TRACKING PROBLEM IN
AFFINE NONLINEAR SYSTEMS

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


Abstract. This paper deals with a general tracking problem for affine nonlinear systems. The approach is quite general. In fact, a Lyapunov function is chosen and a stabilizing structure of the solution to solve a general tracking problem is proposed. Nevertheless, the general final solution is a discrete one and consists of an approximation of the continuous solution. Moreover, there is an assumption which should be guaranteed in order to obtain the explicit expression of the digital final solution. Despite this assumption the solution remains valid for a wide range of applications according to practical tests. The importance of the solution consists of its generality. In fact, any kind of nonlinearity could be taken into account. Also technical nonlinearities such as hysteresis, saturations, and creep could be considered.

Received: October 23, 2012

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

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

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 5