The input π₯[π] and output π¦[π] of a discrete-time system are related as
Q. The input π₯[π] and output π¦[π] of a discrete-time system are related as π¦[π] = πΌπ¦[π β 1] + π₯[π]. The condition on πΌ for which the system is Bounded-Input Bounded-Output (BIBO) stable is
(A) |πΌ| < 1
(B) |πΌ| = 1
(C) |πΌ| > 1
(D) |πΌ| < 3/2
Ans: |πΌ| < 1
Sol:
y[n] = Ξ± y[n β 1] + x [n]
The given system is BIBO stable for |Ξ±| < 1