[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

316 A. Czornik, A. Nawrat, and M. Niezabitowski
2
(n 2 + 20) 2 + 4√ ∣
2 ∣∣∣
n 2 + 20 |cosn| + 4 cos 2 n − 1 ]
2 ∣ =
2
∣ sin2 n − 1 2 ∣ + 2√ 2
n 3 + 10 |sinn| + 1
(n 3 + 10) 2 +
1
(n 2 + 20) 2 + 2√ ∣
2 ∣∣∣
n 2 + 20 |cosn| + 2 cos 2 n − 1 2∣
varies between 0 and 2.5 it implies that for any solution x(n,x 0 ) of system (1) only
the upper estimate (7)
‖x(n + 1,x 0 )‖≤‖x 0 ‖
n
∏
p=0
√
(b(p)+1)
is valid for all n. The numerical values of the solution and bound are presented in
Figure (1)
Fig. 1. Our upper estimate and values of norms of matrix products
From this example we can only estimate an upper bound for growth rate.
Example 2. Consider system (1) with (A(n)) n∈N given by
[ ]
sinn
1
A(n)=
n 3 +10
1
n 2 +20 cosn .