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Stability of a class of adaptive nonlinear systems

100%
Dzielinski A.
International Journal of Applied Mathematics and Computer Science
|
2005
|
tom 15
|
nr 4
455-462
EN
This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear systems is investigated and it is shown how the problem of model following control may be tackled using this methodology.
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Normalized finite fractional differences: Computational and accuracy breakthroughs

88%
Stanisławski R., Latawiec K.
International Journal of Applied Mathematics and Computer Science
|
2012
|
tom 22
|
nr 4
907-919
EN
This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with the introduction of a perfect finite fractional difference and, in particular, a powerful adaptive finite fractional difference, whose excellent performance is illustrated in simulation examples.
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