TIFR ECE 2020 | Question: 1

Question

Consider a discrete-time system which in response to input sequence $x[n] \;( n$ integer) outputs the sequence $y[n]$ such that

\[y[n]=\left\{\begin{array}{ll}
0, & n=-1,-2,-3, \ldots, \\
\alpha y[n-1]+x[n]+1, & n=0,1,2, \ldots
\end{array}\right.\]

Suppose $|\alpha|<1$. Is the system linear, time-invariant, bounded input bounded output (BIBO) stable?

• A. Linear, time-invariant, BIBO stable
• B. Non-linear, time-invariant, BIBO stable 
• C. Linear, time-variant, BIBO unstable
• D. Non-linear, time-variant, BIBO stable
• E. Cannot be determined from the information given