The following are all methods of checking the stability of discrete-time systems excepta.Routh-Hurwitz Criterionb.None of the optionsc.Jury's Testd.Schur-Cohn Test

For each of the following discrete time systems, where y[n] and x[n] are respectively theoutput and input sequences, determine whether the system is (i) linear, (ii) causal, (iii)stable and (iv) shift-invariant.(a) y[n] = n2x[n],(b) y[n] = x4[n],(c) y[n] = αx[-n], α is a non-zero constant and(d) y[n] = x[n-5]e) y[n] = x[2n]f) y[n] = x[n]x[n-1]

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 statements are true about parameter stability tests?(i)  Parameter stability tests test the assumption that the estimated parameters of a model are constant for the entire sample(ii) Chow test and predictive failure tests are two types of parameter stability tests(iii) Backward and forward predictive failure tests are two types of parameter stability tests(iv) Parameter stability tests examine violations of the classical linear regression model assumptionsGroup of answer choices(i), (ii), (iii) and (iv)(i), (ii) and (iii) only(i) only(i) and (ii) only

What are the general criteria for achieving unconditional stability?a.K>1 and |Δ||Δ|<1b.K<1 and |Δ||Δ|<1c.K>1 and |Δ||Δ|>1d.K<1 and |Δ||Δ|>1

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