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A robust stability assessment approach is presented to efficiently estimate eigenvalues in microgrids in the presence of bounded uncertainties. Through this method, all possible locations of eigenvalues can be directly obtained, which makes repeatedly eigenvalue calculation unnecessary when dealing with uncertainties. More importantly, a quasi-diagonalization technique is established to reduce the...
The stability of fractional-order nonlinear system is still an open problem. In this paper, the stability issue of the positive nonlinear fractional-order population growth model is investigated by using the distributed-order approach and the Lyapunov method. The unconditionally stability is derived, and it is shown that the fact of stability for the equilibrium of fractional-order population growth...
This paper discusses the stability issues of fractional-order nonlinear scalar systems by using the distributed-order operators and the order sensitivity method. A positivity check method is proposed by the use of initialized fractional calculus. By doing so, the fractional-order system is converted to a corresponding distributed-order one, and a group of Lyapunov function candidates of the distributed-order...
The calculation of eigenvalues and eigenvectors plays an important role in the stability analysis and optimal design of microgrids with multiple distributed energy resources. Microgrid systems are usually operated in various uncertain conditions. In this paper, a novel approach based on matrix perturbation theory is proposed for the calculation and analysis of eigenvalues and eigenvectors in a microgrid...
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