Recent content by Aerostd

Something seemed fishy to me, so I went back to this and found a mistake. I need your help to see if what I have done this time is correct and legal. I'll start from the top again. -- Show that x(k) goes to zero in the limit. Let ϵ>0. Now, we know that 0.5k and u(k) both go to zero(by...

-- Show that x(k) goes to zero in the limit. Let \epsilon > 0 . Now, we know that 0.5^{k} and u(k) both go to zero, therefore, for all \epsilon_{1} > 0 , there exists k_{1}>0, such that if k > k_{1}, then | 0.5^{k} | < \epsilon_{1} and | u(k) | < \epsilon_{1}. Now x(k) = | 0.5^{k}...

Sorry about that. I understand and can solve it now. Thanks.

Hi. Thanks a lot for replying. If I replace 0.5^{i}u(k-i) by M where M is it's max value, then I can get an upper bound on x(k). But this upper bound might blow up as k tends to infinity (for the case where M>1). I won't be able to conclude what happens to x(k) as k tends to infinity.

Homework Statement Hello. I am trying to prove a result that I have been making use of, but never really proved. Consider the recurrence equation x(k+1) = 0.5 x(k) + u(k), where u(k) is a bounded sequence. For this problem, assume that u(k) goes to zero. I want to prove that x(k) goes to...

Actually I just thought of one. Thanks. :confused: as always.

Homework Statement Let x_{n} = y_{n} + z_{n} Also, x_{n}>0 , y_{n}>0 , z_{n}>0 . We also know that x_{n} converges. Prove that y_{n} converges. Homework Equations I want to use the Cauchy criterion because the limits are not given. So start with an [tex] \epsilon >0 [/itex]...

Hi, I had a question about understanding some basic thing about the Hausdorff dimension. Specifically, I'm trying to understand why the two dimensional Hausdorff dimension of a 1-d line is zero. In terms of the two dimensional Lebesgue measure, I can see that I can cover the line by a...

I think your system has two degrees of freedom. You should have two differential equations, one for acceleration of x_{1} and one for acceleration of x_{2}. Also, It seems from the problem statement that you have one input f, and two outputs x_{1} and x_{2}. Which means that you should have...

Thanks a lot. I guess now I will move on to the next page in the book. I don't know if I should open a new thread or not but here goes. This is Proposition 1.3 in Folland. I am interested more in the notation than in the proof given in the book. The proposition is If A is countable, then the...

Homework Statement I should mention beforehand that I do not come from a math background so I may ask some trivial questions. I am reading the book "Real Analysis" by Folland for a course I am taking and am attempting to understand a definition of product sigma algebra. It is stated in the...

Homework Statement I think I will start with the figure below: The wire of infinite length rotates about the point "a" with constant angular speed. The bead starts out at rest. There is no friction or gravity. I have already derived the equations of motion for this system (I used...

My question is that if two different initial conditions give you the same free response, doesn't that violate the definition of a state?

Homework Statement I have set up this problem for myself. Let P be a system of the form x' = Ax + Bu y = Cx + Du The definition of a "state" is: "x(t) is a state for a system P if knowledge of x at some initial time t_{0} and the input u(t), t \geq t_{0} is sufficient to uniquely determine...

Homework Statement This is not a homework problem. I encountered this while working with total least squares for the first time. Ultimately a point is reached where Az=0 must be solved. z is of the form [x,1]^{T}. Let A be nxm, z be mx1. Suppose A is rank deficient by one. So the SVD of A...