The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order, Mathematics in Science and Engineering, 1974. ,

, Systèmes asservis linéaires d'ordre fractionnaire, 1983.

, La commande CRONE, 1991.

Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay, special Issue on Advances in Fractional Differential Equations II, vol.62, pp.1531-1539, 2011. ,

Discrete fractional kalman filter, IFAC Pro-270 ceedings Volumes, 2nd IFAC Conference on Intelligent Control Systems and Signal Processing, vol.42, pp.520-525, 2009. ,

, International Multi-Conference on Systems, Sygnals Devices, pp.1-6, 2012.

Observer for discrete fractional order state-space systems, 2nd IFAC Workshop on Fractional Differentiation and its Applications, vol.39, pp.511-516, 2006. ,

Interval state estimation for a class of nonlinear systems, IEEE Transactions on Automatic Control, vol.57, issue.1, pp.260-265, 2012. ,

Interval observers for time-varying discrete-time 280 systems, IEEE Transactions on Automatic Control, vol.58, issue.12, pp.3218-3224, 2013. ,

Interval Observers for Discrete-time Systems, International Journal of Robust and Nonlinear Control, vol.24, issue.17, pp.2867-2890, 2014. ,

URL : https://hal.archives-ouvertes.fr/hal-00761600

, LMI stability conditions for fractional order systems, vol.59, pp.1594-1609, 2010.

URL : https://hal.archives-ouvertes.fr/hal-00368173

Equivalence of history-function based and infinitedimensional-state initializations for fractional-order operators, ASME Journal of computational and nonlinear dynamics, vol.8, issue.4, 2013. ,

Initial conditions and initialization of linear fractional differential equations, Signal Process, vol.91, pp.427-436, 2011. ,

Initialization in fractional order systems, European Control Conference (ECC), pp.1471-1476, 2001. ,

Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, 1999. ,

, Fractional Differential Equations, 1999.

A solution to the fundamental linear fractional order differential equation, NASA/TP-1998-208693 report, 1998. ,

Optimal fractional-order damping, ASME IDETC/CIE Conferences, 2003. ,

A note on L p -norms of fractional systems, Automatica, vol.49, issue.9, pp.2923-2927, 2013. ,

Coprime factorizations and stability of fractional differential systems, Systems & Control Letters, vol.41, issue.3, pp.167-174, 2000. ,

Stability properties for generalized fractional differential systems ,

, Systèmes Différentiels Fractionnaires -Modèles, Méthodes et Applications 5

Stability and resonance conditions of elementary fractional transfer functions, Automatica, vol.47, issue.11, pp.2462-2467, 2011. ,

URL : https://hal.archives-ouvertes.fr/hal-00668249

Andréa Novel, Some results on controllability and observability of finite-dimensional 310 fractional differential systems, IMACS, vol.2, pp.952-956, 1996. ,

Andréa Novel, Observer-based controllers for fractional differential systems, 36th IEEE Conference on Decision and Control, pp.4967-4972, 1997. ,

A note on the controllability and the observability of fractional dynamical systems, 2nd IFAC Workshop on Fractional 315 Differentiation and its Applications, vol.39, pp.493-498, 2006. ,

On observability and pseudo state estimation of fractional order systems, European Journal of Control, vol.18, issue.3, pp.260-271, 2012. ,

URL : https://hal.archives-ouvertes.fr/hal-00787240

, Discrete-time fractional-order systems: Modeling and stability issues, 2012.

Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems, Bulletin of the Polish Academy of Sciences Technical Sciences, issue.4, p.61 ,

Controllability and observability of linear discrete-time fractional-order systems, International Journal of Applied Mathematics and Computer Science, vol.18, issue.2 ,

On Robust Pseudo State Estimation of Fractional Order Systems, pp.97-111, 2017. ,

Differentiation similarities in fractional pseudo-state space representations and the subspace-based methods, Fractional Calculus and Applied Analysis, vol.16, pp.273-287, 2013. ,

URL : https://hal.archives-ouvertes.fr/hal-00804801

Stable interval observers in bbc for linear systems with time-varying input bounds, IEEE Transactions on Automatic Control, vol.58, issue.2, pp.481-487, 2013. ,

, Fractional Linear Systems and Electrical Circuits, 2014.

, Q: stands for reviewer's Question or Comment. R: stands for authors' response

, Q: Reviewed paper deals with an interval observer which is synthesized for fractional linear systems with additive noise and disturbances. Some corrections are necessary. R: The reviewer is gratefully acknowledged for his careful reading, encouragements, and guidance for improving the manuscript

, definition of binomial coefficients in form of factorial (2) cannot be used, it is valid only for integer number, not real one, rather use definition by Gamma function. R1: Since j is an integer, the presented definition of Newton binomial is correct. The 470 authors do not use factorial of ?. The definition of Newton's binomial exists and is an alternative for the previous version of equation (2). As suggested by the reviewer, the two definitions of Newton, Q1. Since order ? is real, defined in (1)

, Laplace transform (3) is valid for all kind of definitions, but only for zero initial 475 conditions. R2: The reviewer is completely right, Q2

, )) is called Grünwald-Letnikov, Q3. approximation

, R3: The authors agree fully with the reviewer and the sentence pointed out has been modified. Check the sentence in red

) legend is not readable, check also other figures. R4: As suggested by the reviewer ,

, Example 1: why you use different notation for fractional derivative in (40) than notation in (4)? R5: As advised by the reviewer, a unique notation of fractional derivative is now used in equations (4) and (40), Q5

, Q6. check References