Controllability and observability of fuzzy matrix discrete dynamical systems
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 12, p. 816-828.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, sufficient conditions for the controllability of the fuzzy dynamical discrete system with the use of fuzzy rule base are established. Further, a sufficient condition for the fuzzy dynamical discrete system to be observable is constructed. The main advantage of this approach is that the rule base for the initial value can be determined without actually solving the system. Difference inclusions approach is adopted in the construction of these conditions. All the established theories are consolidated and explained with the help of examples.
DOI : 10.22436/jnsa.012.12.04
Classification : 93B05, 93C55, 93C42, 93B07
Keywords: Fuzzy difference equations, fuzzy rule, controllability, observability, discrete dynamical systems

Rompicharla, Charyulu L. N.  1 ; Putcha, Venkata Sundaranand  2 ; Deekshithulu, G. V. S. R.  3

1 Department of Mathematics, V. R. Siddhartha Engineering College, Kanuru, Vijayawada-520007, A. P., India
2 Department of Mathematics, Rayalaseema University, Kurnool-518007, A. P., India
3 Department of Mathematics, JNTU College of Engineering, Kakinada, A. P., India
@article{JNSA_2019_12_12_a3,
     author = {Rompicharla, Charyulu L. N.  and Putcha, Venkata Sundaranand  and Deekshithulu, G. V. S. R. },
     title = {Controllability and observability of fuzzy matrix discrete dynamical systems},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {816-828},
     publisher = {mathdoc},
     volume = {12},
     number = {12},
     year = {2019},
     doi = {10.22436/jnsa.012.12.04},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.12.04/}
}
TY  - JOUR
AU  - Rompicharla, Charyulu L. N. 
AU  - Putcha, Venkata Sundaranand 
AU  - Deekshithulu, G. V. S. R. 
TI  - Controllability and observability of fuzzy matrix discrete dynamical systems
JO  - Journal of nonlinear sciences and its applications
PY  - 2019
SP  - 816
EP  - 828
VL  - 12
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.12.04/
DO  - 10.22436/jnsa.012.12.04
LA  - en
ID  - JNSA_2019_12_12_a3
ER  - 
%0 Journal Article
%A Rompicharla, Charyulu L. N. 
%A Putcha, Venkata Sundaranand 
%A Deekshithulu, G. V. S. R. 
%T Controllability and observability of fuzzy matrix discrete dynamical systems
%J Journal of nonlinear sciences and its applications
%D 2019
%P 816-828
%V 12
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.12.04/
%R 10.22436/jnsa.012.12.04
%G en
%F JNSA_2019_12_12_a3
Rompicharla, Charyulu L. N. ; Putcha, Venkata Sundaranand ; Deekshithulu, G. V. S. R. . Controllability and observability of fuzzy matrix discrete dynamical systems. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 12, p. 816-828. doi : 10.22436/jnsa.012.12.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.12.04/

[1] Alwadie, A.; Ying, H.; Shah, H. A Practical two-input two-output Takagi-Sugeno fuzzy controllers, Int. J. Fuzzy Syst., Volume 5 (2003), pp. 123-130

[2] Anand, P. V. S.; Murty, K. N. Controllability and Observability of Liapunov type matrix difference system, Proceedings of $50^{th}$ Congress of ISTAM (An International Meet) IIT Kharagpur, Volume 2005 (2005), pp. 125-132

[3] Barnett, S.; Cameron, R. G. Introduction to Mathematical Control Theory, The Clarendon Press-Oxford University Press, New York, 1985

[4] Chen, Y.; Yang, B.; Abraham, A.; Peng, L. Automatic design of hierarchical takagi-sugeno type fuzzy systems using using evolutionary algorithms, IEEE Trans. Fuzzy Syst., Volume 15 (2007), pp. 385-397 | DOI

[5] Conway, J. B. A Course in Functional Analysis, Springer-Verlag, New York, 1990 | DOI

[6] Ding, Z. H.; Kandel, A. On the observability of fuzzy dynamical Control systems (II), Fuzzy Sets and Systems, Volume 115 (2000), pp. 261-277 | Zbl | DOI

[7] Ding, Z. H.; Kandel, A. On the observability of fuzzy dynamical control systems (II), J. Fuzzy Math., Volume 18 (2000), pp. 295-306

[8] Ding, Y. S.; Ying, H.; Shao, S. H. Structure and stability analysis of a Takagi-Sugeno fuzzy PI Controller with application to tissue hyperthermia therapy, Soft Computing, Volume 2 (1999), pp. 183-190 | DOI

[9] Ding, Y. S.; Ying, H.; Shao, S. H. Typical Takagi-Sugeno PI and PD fuzzy controllers:analytical structure and stability analysis, Inform. Sci., Volume 151 (2003), pp. 245-262 | DOI

[10] Johansen, T. A.; Shortern, R.; Murray-Smith, R. On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models, IEEE Trans. Fuzzy Syst., Volume 8 (2000), pp. 297-313 | DOI

[11] Murty, K. N.; Anand, P. V. S. Controllability and Observability of Continuous Matrix Liapunov Systems, in: Advances in Nonlinear Dynamics, Volume 1997 (1997), pp. 365-379 | Zbl

[12] Murty, K. N.; Andreou, S.; Viswanadh, K. V. K. Qualitative properties of general first order matrix difference systems, Nonlinear Stud., Volume 16 (2009), pp. 359-370 | Zbl

[13] Murty, K. N.; Balaram, V. V. S. S. S.; Viswanadh, K. Solution of Kronecker Product Initial Value Problems Associated with First Order Difference System via Tensor--based Hardness of the Shortest Vector Problem, Electronic Modeling, Volume 30 (2008), pp. 18-33

[14] Negoita, C. V.; Ralescu, D. A. Applications of Fuzzy Sets to Systems Analysis, Birkhäuser, Basel, 1975 | Zbl | DOI

[15] Sugeno, M. On Stability of fuzzysystems expressed by fuzzy rules with singleton consequents, IEEE Trans. Fuzzy Syst., Volume 7 (1999), pp. 201-224 | DOI

[16] Takagi, T.; Sugeno, M. Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man Cybern., Volume 15 (1985), pp. 116-132 | Zbl | DOI

[17] Ying, H. Analytical analysis and feedback linearization tracking control of the general Takagi-Sugeno fuzzy dynamic systems, IEEE Trans. Syst. Man Cybern. Part C, Volume 29 (1999), pp. 290-298

[18] Ying, H. Deriving analytical input-output relationship for fuzzy controllers using arbitraty input fuzzy sets and Zadeh fuzzy AND operator, IEEE Trans. Fuzzy Syst., Volume 14 (2006), pp. 654-662 | DOI

Cité par Sources :