The steady-state solution of stable systems is due to simple pole in the j-Omega axis of the s-plane coming from the input. Suppose the transfer function of the system is

H(s) = Y(s)/X(s) = 1 / [(s+1)^2 + 4]

(a) Find the poles and zeros of H(s) and plot them in the s-plane. Find then the corresponding impulse response h(t). Determine if the impulse response of this system is absolutely integrable so that the system is BIBO stable.

(b) Let the input x(t) = u(t). Find y(t) and from it determine the steady-state solution.

(c) Let the input x(t) = tu(t). Find y(t) and from it determine the steady-state response. What is the difference between this case and the previous one?

(d) To explain the behavior in the case above consider the following: Is the input x(t) = tu(t) bounded? That is, is there some finite value M such that |x(t)| < M for all times? So what would you expect the output to be knowing that the system is stable?

See attached file for problem details.
1. A system has the transfer function:
H(z) = (z2-3z+1)/(z3+ z2-0.5z+0.5)
Is the system stable, marginally stable, or unstable?
2. A discrete-time system is give by the input/output difference equation:
y[n+2]-y[n+1]+y[n]=x[n+2]-x[n+1]
Is the system stable, marginally stab

Given poles(in complex notation) are mapped to both the z and s (Laplace) planes. The transforms between the different planes are developed and the mappings grpahically shown for a number of examples.
See the attached file.

Question 1:
a) Construct the root-locus for the K > 0 for the transfer function
GH = K / [s(s+1)(s^2+7s+12)
b) If the design value for the gain is K = 6, calculate the gain margin.
c) Determine the value of the gain factor K for which the system with the above open loop transfer has closed loop poles with a damping ra

Here is the specific question:
A landscape architect is drawing plans for a rigid lightweight canopy to provide shade for a patio. Two poles will support the canopy. On the drawing, the coordinates of the verticies of the canopy are:
P (0,0)
Q ( 2,3)
R (8, -1)
and S (6, -4)
What are the best places to put the two sup

Skip (a). See attached file for full problem description.
Part (b) only:
Now assume that R1 = R2 = 2 kohms. Choose the values of C1 and C2 so that the transfer function has the poles indicated in figure (b) above.

(b) A particular system has the open loop transfer function:
g(s) = (s+4)/((s+1)(s-2))
sketch the root locus for this system
(c) The system is placed in a feedback control system as shown in Figure Q6. Determine the gain, k, which would result in marginal stability. Determine the frequency of oscillation which would res

A linear time-invariant discrete-time system has transfer function
h(z)=((z^2)-z-2)/((z^2) + 1.5z-1)
a. Use MATLAB to obtain the poles of the system. Is the system stable?
Explain.
b. Compute the step response. This should be done analytically, but you can
use MATLAB commands like conv and residue.
c. Plot the first seve