Advanced Search

Question: Upper bound function

Question:Upper bound function

Zeineb 520 Maple
limit
October 25 2018
0

Hi

I hope everyone is fine.

Here is a nice question :

I have an inequality ( please see maple code) if I assume a special condition (on |f(u,s)| used in the code )

how can I get an upper bound of the function |x(t)| and is the upper bound converges to zero when t goes to infinity.

Maybe this is can be done using maple because by hand up to know I can't find an upper bound which converges to zero as t goes to infinity.

Maybe, there is  a good, nice and appropriate answer using maple.

Below, please find the upper_bound.mw code.

Many thinks

 

Upper_bound.mw


 

``

> 

restart; assume*(0 < gamma); assume*(0 < M)

(0 < gamma)*assume

  

(0 < M)*assume

 (1)
> 

abs(x(t)) <= exp(-gamma*t)*abs(x(0))+int(abs(x(s))*(int(exp(-gamma*(t-u))*abs(f(u, s)), u = s .. t)), s = 0 .. t);

abs(x(t)) <= exp(-gamma*t)*abs(x(0))+int(abs(x(s))*(int(exp(-gamma*(t-u))*abs(f(u, s)), u = s .. t)), s = 0 .. t)

 (2)
> 

> 

assume*(int(abs(f(u, s)), u = 0 .. infinity) < M)

(int(abs(f(u, s)), u = 0 .. infinity) < M)*assume

 (3)
> 

``

 

(I*Can*get*an*upper*bound*of*abs(x(t))*when*I)*assume; int(abs(f(u, s)), u = 0 .. infinity) < M


 

Download Upper_bound.mw
Please Wait...