Introduction to Stability

Q. The open loop transfer function of an unity feedback open loop system is $\frac{2s^2+6s+5}{(s+1{)}^2(s+2)}$. The characteristic equation of the closed loop system is

1. $2s^2+6s+5=0$
2. $(s+1{)}^2(s+2)=0$
3. $2s^2+6s+5+(s+1{)}^2(s+2)=0$
4. $2s^2+6s+5-(s+1^2)(s+2)=0$

Q. The closed loop system of figure is stable if the transfer function $T\left(s\right)=\frac{C\left(s\right)}{R\left(s\right)}$ _____.

1. has all the close loop zeros in left half of the s-plane.
2. has all the close loop poles in left half of the s-plane.
3. has one of the close loop pole in right half of the s-plane.
4. Data insufficient

Q. The system shown in the figure is

1. Stable
2. Unstable
3. conditionally stable
4. stable for input $u_1$, but unstable for input $u_2$