Given only the pole locations, you generally cannot say whether a system is stable or not, unless the poles are on the imaginary axis (the unit circle), in which case the system is unstable. In both cases the region of convergence (ROC) is essential. The imaginary axis of the $s$-plane corresponds to the unit circle in the $z$-plane, and the region inside the unit circle in the $z$-plane corresponds to the left half-plane of the the $s$-plane. The system will be an overdamped systemĬlarification: The system will be a purely oscillatory system with no damping involved.There is no principal difference between continuous-time and discrete-time systems when judging stability. The system will turn out to be critically dampedī. What is the consequence of marginally stable systems?Ī. Hence, the system resolves to be a stable one.ġ0. Comment on the stability of the following system, y = (x) n.Ĭlarification: Even if we have a bounded input as n tends to inf, we will have an bounded output. Hence, the system resolves to be an unstable one.ĩ. Comment on the stability of the following system, y = n*x.Ĭlarification: Even if we have a bounded input as n tends to inf, we will have an unbounded output. Ĭlarification: The integral of the system from -inf to +inf equals to a finite quantity, hence it will be a stable system.Ĩ. Is the system h(t) = exp(-jwt) stable?Ĭlarification: If w is a complex number with Im(w) < 0, we could have an unstable situation as well. Only if it is zero/finite it is stable.Ħ. When a system is such that the square sum of its impulse response tends to infinity when summed over all real time space,Ĭlarification: The system turns out to be unstable. For a bounded function, is the integral of the odd function from -infinity to +infinity defined and finite?Ĭlarification: The odd function will have zero area over all real time space.ĥ. For what values of k is the following system stable, y = (k 2 – 3k -4)log(x) + sin(x)?Ĭlarification: The values of k for which the logarithmic function ceases to exist, gives the condition for a stable system.Ĥ. State whether the integrator system is stable or not.Ĭlarification: The integrator system keep accumulating values and hence may become unbounded even for a bounded input in case of an impulse.ģ. Thus the sin function always stays between -1 and 1, and is hence stable.Ģ. In a,b,d there are regions of x, for which y reaches infinity/negative infinity. Which of the following systems is stable?Ĭlarification: Stability implies that a bounded input should give a bounded output. Signals & Systems Multiple Choice Questions on “BIBO Stability”.ġ.
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