Oscillations in fractional order LTI systems: Harmonic analysis and further results

Authors:
Milad Siami;Mohammad Saleh Tavazoei
Affiliations:
Electrical Engineering Department, Sharif University of Technology, Tehran, Iran;Electrical Engineering Department, Sharif University of Technology, Tehran, Iran
Venue:
Signal Processing
Year:
2013

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Abstract

This paper studies undamped oscillations generated by marginally stable fractional order linear time invariant (LTI) systems. In this study, an analytical approach is proposed to be used for harmonic analysis of such oscillations in marginally stable commensurate order LTI systems. Also, it is shown that the Q-semi norm of the limit sets for a trajectory of these systems can be analytically determined based on the Q-semi norm of the initial condition, where Q is a specific matrix. Moreover, this result is extended to the wider class of rational order systems. Finally, some numerical examples are presented to demonstrate the use of the paper results.