Which of the following systems is stable?
Stability implies that a bounded input should give a bounded output. In a,b,d there are regions of x, for which y reaches infinity/negative infinity. Thus the sin function always stays between -1 and 1, and is hence stable.
State whether the integrator system is stable or not.
The integrator system keep accumulating values and hence may become unbounded even for a bounded input in case of an impulse.
For what values of k is the following system stable, y = (k2 – 3k -4)log(x) + sin(x)?
The values of k for which the logarithmic function ceases to exist, gives the condition for a stable system.
For a bounded function, is the integral of the odd function from -infinity to +infinity defined and finite?
The odd function will have zero area over all real time space.
When a system is such that the square sum of its impulse response tends to infinity when summed over all real time space,
The system turns out to be unstable. Only if it is zero/finite it is stable.
Is the system h(t) = exp(-jwt) stable?
If w is a complex number with Im(w) < 0, we could have an unstable situation as well. Hence, we cannot conclude [no constraints on w given].
Is the system h(t) = exp(-t) stable?
The integral of the system from -inf to +inf equals to a finite quantity, hence it will be a stable system.
Comment on the stability of the following system, y[n] = n*x[n-1].
Even if we have a bounded input as n tends to inf, we will have an unbounded output. Hence, the system resolves to be an unstable one.
Comment on the stability of the following system, y[n] = (x[n-1])n.
Even if we have a bounded input as n tends to inf, we will have an bounded output. Hence, the system resolves to be a stable one.
What is the consequence of marginally stable systems?
The system will be a purely oscillatory system with no damping involved.