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Generalized observer design of index one for descriptor systems with unknown inputs

Kumar Abhinav, Gupta Mahendra Kumar

Archives of Control Sciences

2023

Vol. 33, No. 1

83--99

Generalized observers are proposed to relax the existing conditions required to design Luenberger observers for rectangular linear descriptor systems with unknown inputs. The current work is focused on designing index one generalized observers, which can be naturally extended to higher indexes. Sufficient conditions in terms of system operators for the existence of generalized observers are given and proved. Orthogonal transformations are used to derive the results. A physical model is presented to show the usefulness of the proposed theory.

The Generalized Differential Transform Method for solution of a free vibration linear differential equation with fractional derivative damping

Das Deepanjan

Journal of Applied Mathematics and Computational Mechanics

2019

Vol. 18, nr 2

19--29

In the present paper, the Generalized Differential Transform Method (GDTM) is used for obtaining the approximate analytic solutions of a free vibration linear differential equation of a single-degree-of-freedom (SDOF) system with fractional derivative damping. The fractional derivatives are described in the Caputo sense.