Abstract
A generalised applied of two modified update laws to plant model of relative degree greater than one, for variable structure model reference adaptive control, is presented in this paper. A type of augmented error is involved as identifier error. A k-sigmoid function, in parameter update laws, is used for to avoid stability analysis of the closed loop described by differential equations with discontinuous right-hand side. A forgetting term, that does not require any prior information, is enclosed in parameter update laws of the control input for to improve the transitory response and robustness to disturbances and unmodeled dynamics. Stability proof of the closed loop and on-line identifier is given together with the condition for system evolution in sliding mode.
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