Using an appropriate definition of the multiplicity of a spectral value, we introduce a new definition of the trace and determinant of elements with finite spectrum in Jordan-Banach algebras. We first extend a result obtained by J. Zemánek in the associative case, on the connectedness of projections which are close to each other spectrally (Theorem 2.3). Secondly we show that the rank of the Riesz projection associated to a finite-rank element a and a finite subset of its spectrum is equal to the sum of the multiplicities of these spectral values (Theorem 2.6). Then we turn to the study of properties such as linearity and continuity of the trace and multiplicativity of the determinant.
This paper addresses the problem of accurately estimating the mechanical and magnetic state variables as well as the stator and rotor resistances of induction motors using only the stator current measurements and the supplied stator voltages from an appropriate nonlinear parametrization. The involved estimation is carried out by a high gain adaptive observer designed bearing in mind the available fundamental results together with the useful implementation features, namely conception simplicity and computational efficiency. An exponential convergence of the state and parameter estimation errors is established under admissible assumptions, namely the persistent excitation requirement has been particularly reduced thanks to the introduction of unknown parameter characteristic indices. The effectiveness of the adaptive observer is highlighted throughout simulation results involving a typical induction motor.
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