Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 12 (2019), 816–828 Research Article ISSN: 2008-1898 Journal Homepage: www.isr-publications.com/jnsa Controllability and observability of fuzzy matrix discrete dynamical systems Charyulu L. N. Rompicharla a , Venkata Sundaranand Putcha b,* , G. V. S. R. Deekshithulu c a Department of Mathematics, V. R. Siddhartha Engineering College, Kanuru, Vijayawada-520007, A. P., India. b Department of Mathematics, Rayalaseema University, Kurnool-518007, A. P., India. c Department of Mathematics, JNTU College of Engineering, Kakinada, A. P., India. Abstract 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. Keywords: Fuzzy difference equations, fuzzy rule, controllability, observability, discrete dynamical systems. 2010 MSC: 93B05, 93C55, 93C42, 93B07. c 2019 All rights reserved. 1. Introduction Measurements of data or speciﬁed information for an underlying problem may be imprecise or only partially speciﬁed. Each and every practical system is endowed with uncertainties. The more the com- plexity of a system the greater is its uncertainty due to fuzziness. That is, each quantity we want to measure becomes fuzzy valued instead of precise valued. Difference equations describe the evolution of certain phenomena over the course of time. Many of the physical applications may not have the exact information about their deterministic dynamics which is a prerequisite construct of a dynamical system. It is very important to study the controllability and obsarvability of the mathematical models represented by fuzzy difference equations governing the ambiguity in dynamics which is not probabilistic. In general the problem of steering an initial state of a system to a desired ﬁnal state in R n become a problem of steering a fuzzy-state to another fuzzy-state in (E l ) n . The importance of control theory in mathematics and its occurrence in several problems such as mechanics, electromagnetic theory, thermodynamics, and artiﬁcial satellites are well known. In general, * Corresponding author Email addresses: narayanarompicharla@gmail.com (Charyulu L. N. Rompicharla), anand_putcha@yahoo.com (Venkata Sundaranand Putcha), deekshitulu_g@yahoo.com (G. V. S. R. Deekshithulu) doi: 10.22436/jnsa.012.12.04 Received: 2019-06-05 Revised: 2019-07-01 Accepted: 2019-07-23