when the output is bounded for bounded inputs, then the system is said to be a)stable b) unstable c)functional d) unfunctional please explain

For each of the following statements determine whether it is True or False. Providedetailed analysis and rationale with appropriate drawings and/or equations.(1+4) x 4= 20(a) A system with a transfer function 𝑎𝑎𝑠𝑠+𝑏𝑏 can be stable if b < 0.(b) The system with transfer function 𝑐𝑐𝑠𝑠 2 +𝑏𝑏𝑠𝑠+𝑐𝑐 is a critically damped system, if 𝑐𝑐 = 𝑏𝑏 24 .(c) Consider the feedback system in Figure 2, if controller C is chosen to be a proportionalcontroller, then the system output can never track the reference, i.e., |e| = |Yref −Y| > 0.(d) For the feedback system in Figure 2, consider the controller C is a proportional-integralcontroller with proportional gain 𝐾𝐾𝑃𝑃 and integral gain 𝐾𝐾𝐼𝐼. If for the system a =1 andthe integral gain is chosen to be 𝐾𝐾𝐼𝐼 > (𝑏𝑏+𝐾𝐾𝑃𝑃)24 , the system will possess underdampedbehaviour

Which of the following is true about unstable asynchronous sequential circuits?a.They have bounded outputb.They are impossible to stabilizec.They exhibit divergent behavior over timed.They always lead to circuit failure

a linear second order single input continuous time system is described by following set of differential equation:x1(t) = -2x1(t) + 4x2 (t)x2(t) = 2x1(t) - x2 (t) + u(t)where x1(t) and x2(t) are state variable and u(t) is the control variable..................the system is:(a)controllable and stable(b)controllable but unstable(c)uncontrollable and unstable(d)uncontrollable but stable

Transient response analysis is done for_________ systems. Question 5Answer a. Stable b. Unstable c. Marginally stable d. Conditionally stable

Which of the following is a characteristic of a stable asynchronous sequential circuit?a.Exponential growthb.Damped responsec.Unbounded outputd.Oscillatory behavior