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Algorithms 2018, 11(9), 136; https://doi.org/10.3390/a11090136

Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

1
Department of Electrical Engineering, University of Chile, Av. Tupper, Santiago 2007, Chile
2
Advanced Mining Technology Center, University of Chile, Av. Tupper, Santiago 2007, Chile
3
Department of Electricity, Universidad Tenológica Metropolitana, Av. José Pedro Alessandri, Santiago 1242, Chile
4
Department of Electrical Engineering, CINVESTAV, Av. IPN, México DF 2508, Mexico
*
Author to whom correspondence should be addressed.
Received: 9 June 2018 / Revised: 5 September 2018 / Accepted: 7 September 2018 / Published: 9 September 2018
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Abstract

Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers. View Full-Text
Keywords: fractional order systems; fractional order observers; fractional order adaptive observers; robust fractional order observers fractional order systems; fractional order observers; fractional order adaptive observers; robust fractional order observers
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Duarte-Mermoud, M.A.; Gallegos, J.A.; Aguila-Camacho, N.; Castro-Linares, R. Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems. Algorithms 2018, 11, 136.

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