Consider the following system whose state space representation is as follows:

x'1 -1 1 α x1 0

x'2 = 0 -2 1 x2 + 0 u

x'3 0 0 -3 x3 1

y = [1 0 0]x

a) Draw the block diagram representation of the system.
b) Find the transfer function of the system.
c) Are there any values of α for which the system would be unstable?
d) Using the transfer function, determine for which value(s) of α the system is unstable.
e) Is the system controllable when α tends to infinity? Explain your answer.
f) Using the controllability matrix, check the answers found in (d) and (e).

Consider the system . It can be shown that there is other state equation possible for this system.
Let us define a new set of state-variables z1 , z2 , z3 by the transformation:
Obtain the state-spacerepresentation of the system in terms of the new variables.
Please see the attached file for the fully formatted problem

Consider the system (see attached file). Determine the transfer function of the system in terms of Laplace transform. Expand the transfer function by means of partial fractions and find your new state equations by means of inverse Laplace transform. Obtain the state-spacerepresentation of the system.

Consider the following system (see attachment) whose statespacerepresentation is as follows:
a) Find the transfer function of the system.
b) Compute eAt using the eigenvalues and eigenvectors method.
c) Compute eAt using the partial fraction method.
d) If u (t)=0 for t ≥ 0,compute x (t), y(t), and x(1) =[ -1 2]T

I need some help with these questions:
2. Calculate the linear statespace matrices A,B,C and D for system that is described by the state equations, for deviations from uop = [-1, 1]^T, xop = [1,1,0]^T and yop= [0] (see attached file for better formula representation).
3. A linear system is described by its transfer funct

Consider the eigenstates of the infinite square well defined by
V(x<-a/2) = infinity
V(-a/2 < x < a/2) = 0
V (x> a/s) = infinity
a. If the Hilbert space base-kets for this potential are seen in the attachment. Write down the matrix representation for the Hamiltonian H-hat of the system.
b. What is the matrix representati

Consider a two state system spanned by two orthonormal vectors, |1> and |2>. The action of an operator Â is defined via:
Â|1> = 2|1> + i|2>
Â|2> = -i|1> + 3|2>
Find Â|ѱ> where
|ѱ> = |1> + |2>
Can you now verify your answer for Â|ѱ> by doing the calculation in matrix representation?
And then compute the fo