The discussion centers on the stability of the systems defined by the equations y(t) = t x(t) and y(t) = x(t)/t. It is established that y(t) = t x(t) can be considered stable under certain conditions where x(t) does not approach infinity. However, as t approaches zero, both systems yield unbounded outputs from bounded inputs, confirming their instability. The consensus is that y(t) = x(t)/t is inherently unstable due to its behavior at t equal to zero.
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kovachattack said:As t approaches zero, you get unbounded outputs from bounded inputs. So, it is unstable.
Also, please somebody correct me if I am wrong, but I believe y(t) = t x(t) does in fact have a bounded output for a bounded input. If you don't let x go to infinity, then y will also not go to infinity, and is therefore bounded and stable.