R. KALMAN `S PROBLEM ABOUT FIBONACCI `S NUMBERS - Iskakova, M.T.; Shuakayev М.К.; Tuiykov Е.А.; Nazarbekova К.Т. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2020)
In this paper authors are considered the R. Kalman`s problem about of Fibonacci numbers. An overview of research methods for control theory systems in two concepts “state space” and the “input-output” mapping is presented. In this paper, we consider the problem of R. Kalman on Fibonacci numbers, which consists in the following. R. Kalman’s problem on Fibonacci numbers is considered, which is as follows. Fibonacci numbers form a minimal Realization. The authors of the article formulated a theorem, which was given the name of the outstanding American Scientist R. Kalman. The proof of the theorem is very cumbersome, therefore, authors proved it using an example when the Fibonacci numbers are obtained on the basis of the application of the B. Ho`s algorithm. B. Ho is a purple of R. Kalman. In this paper, the algorithm of B. Ho is given, which allows one to find the parameters of the initial linear deterministic system. Based on these parameters, we find the initial Fibonacci numbers. Thus, Fibonacci numbers are closely related to the problem of linear deterministic implementation and to B. Ho’s algorithm.