×

On the observability of conformable linear time-invariant control systems. (English) Zbl 1471.93042

Summary: In this paper, we analyze the concept of observability in the case of conformable time-invariant linear control systems. Also, we study the Gramian observability matrix of the conformable linear system, its rank criteria, null space, and some other conditions. We also discuss some properties of conformable Laplace transform.

MSC:

93B07 Observability
93C15 Control/observation systems governed by ordinary differential equations
34A08 Fractional ordinary differential equations
44A10 Laplace transform
93C05 Linear systems in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279, 57-66 (2015) · Zbl 1304.26004
[2] D. Baleanu, Z. B Güvenc and J. A. Tenneiro Machado, New Trends in Nanotechnology and Fractional Calculus Applications, Springer, New York, 2010.
[3] I. Benabbas; D. E. Teniou, Observability of wave equation with Ventcel dynamic condition, Evol. Equ. Control Theory, 7, 545-570 (2018) · Zbl 1405.35103
[4] R. Caponetto, G. Dongola, L. Fortuna and I. Petras, Fractional Order Systems: Modeling and Control Applications, World Scientific Series, vol. 72, 2010,200 pp.
[5] A. Escalante; Al dair-Pantoja, The Hamilton-Jacobi analysis and canonical covariant description for three-dimensional Palatini theory plus a Chern-Simons term, Eur. Phys. J. Plus, 134, 1-10 (2019)
[6] R. Hilfer; L. Anton, Fractional master equations and fractal time random walks, Phys. Rev. E, 51, 1-5 (1995)
[7] R. Khalil; M. Al Haroni; A. Yousef; M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264, 65-70 (2014) · Zbl 1297.26013
[8] R. E. Kálmán, Contributions to the theory of optimal control, Bol. Soc. Mat. Mexicana, 2, 102-119 (1960) · Zbl 0112.06303
[9] R. E. Kálmán, Mathematical description of linear dynamical systems, J. SIAM Control Ser. A, 1, 152-192 (1963) · Zbl 0145.34301
[10] N. A. Khan; O. A. Razzaq; M. Ayyaz, Some properties and applications of Conformable Fractional Laplace Transform (CFLT), J. Fract. Calc. Appl., 9, 72-81 (2018) · Zbl 1488.44004
[11] D. Kumar; J. Singh; K. Tanwar; D. Baleanu, A new fractional exothermic reactions model having constant heat source in porous media with power, exponential and Mittag-Leffler Laws, Int. J. Heat Mass Transf., 138, 1222-1227 (2019)
[12] V. Mohammadnezhad; M. Eslami; H. Rezazadeh, Stability analysis of linear conformable fractional differential equations system with time delays, Bol. Soc. Parana. Mat., 38, 159-171 (2020) · Zbl 1431.34072
[13] K. S. Nisar, G. Rehman and K. Mehrez, Chebyshev type inequalities via generalized fractional conformable integrals, J. Inequal. Appl., 2019 (2019), Paper No. 245, 9 pp. · Zbl 1499.26154
[14] H. Rezazadeh; H. Aminikhah; A. H. Refahi Sheikhani, Stability analysis of conformable fractional systems, Iranian J. Numer. Anal. Opti., 7, 13-32 (2017) · Zbl 1368.34014
[15] W. J. Rugh, Linear System Theory 2E, Prentice Hall, Upper Saddle River, NJ, 07458, 1996. · Zbl 0892.93002
[16] C. Ruiyang; G. Fudong; C. Yangquan; K. Chunhai, Regional observability for Hadamard-Caputo time fractional distributed parameter systems, Appl. Math. Comput., 360, 190-202 (2019) · Zbl 1428.34011
[17] F. S. Silva; D. M. Moreira; M. A. Moret, Conformable Laplace Transform of fractional differential equations, Axioms, 55, 1-11 (2018) · Zbl 1432.34014
[18] E. Unal; A. Gokdogan; E. Celik, Solutions around a regular a singular point of a sequential conformable fractional differential equation, Kuwait Journal of Science, 44, 9-16 (2017) · Zbl 1463.34025
[19] T. A. Yıldız; A. Jajarmi; B. Yıldız; D. Baleanu, New aspects of time fractional optimal control problems within operators with nonsingular kernel, Discrete Contin. Dyn. Syst. Ser. S, 13, 407-428 (2020) · Zbl 1439.49010
[20] D. Zhao and M. Luo, General conformable fractional derivative and its physical interpretation, Calcolo, (2017), 903-917. · Zbl 1375.26020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.