![The input π₯[π] and output π¦[π] of a discrete-time system are related as](https://www.gkseries.com/blog/wp-content/uploads/2023/08/The-input-π₯π-and-output-π¦π-of-a-discrete-time-system-are-related-as-.jpg)
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 – 1] + x [n]
The given system is BIBO stable for |Ξ±| < 1
![The input π₯[π] and output π¦[π] of a discrete-time system are related as](https://www.gkseries.com/blog/wp-content/uploads/thumbs_dir/In-the-Figures-a-and-b-shown-below-the-transformers-are-identical-and-ideal-except-that-the-transformer-in-Figure-b-is-centre-tapped.-Assuming-ideal-diodes-qbkna33yusoriuz3mr9wh5liikubncppyp5ug8c8xo.jpg)
![The input π₯[π] and output π¦[π] of a discrete-time system are related as](https://www.gkseries.com/blog/wp-content/uploads/thumbs_dir/In-a-cascade-control-system-the-closed-loop-transfer-function-of-the-inner-loop-may-be-assumed-to-have-a-single-time-constant-T1-.-Similarly-the-closed-loop-transfer-qbko5wx89u9aniqqs0k4emgen9yrae2io8eqgj5c8s.jpg)
![Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]](https://www.gkseries.com/blog/wp-content/uploads/2023/10/Determine-the-correctness-or-otherwise-of-the-following-Assertion-A-and-the-Reason-R.jpg)
