FNT: Just as "state" in the case of continuous time refers to anything that has a derivative taken in system of differential equations, for discrete time systems, the concept of state refers to memory. at, besides the current input, must you remember about the past/present to be able to figure out the are? In this case, you must know both :(t) and z(t 1).) will now show how the initial matrix representation fon'c'(t) can be converted to the canonical form 'z'(t) using a change of basis . Suppose we do a transformation of the coordinates of the stateit'(t) (t) = P560). Write down the state -transition matrices of'z'(t) in terms of the state transition l 0 at triees of 35(t), i.e., express AZ and 3a in terms of A, B, and P. For P = 1 1:| , conrm that resulting state space representation of the behavior off\") is indeed the same as the previous part . we get the same AHBZ). the previous part, Design a feedback [f-l f2] to place the closed-loop eigenvalues athl : 112: ;. Conrm that [f1 f2] = [fl f2]P. DNUS, but in scope)Here, we gave you theP matrix . How would you have come up with the matrix on your own? (Hint : start with the second column of? and ask where it might have come n . Then , is there a relationship between the coefficients of the difference equation in part (d) to the momial whose roots you need to find in part (b)?) following this technique, any controllable discrete-time system can be converted to the "control- e canonical form " shown in part (d) by finding the right change of coordinates are now ready to go through some numerical examples to see how state feedback works. Consider rst discrete -time linear system . Enter the matrix A and B from (a) for the system 55(t+ 1) = A30) + Bu (t) + w(t) > the Jupyter notebook and use the random input w(t) as the disturbance introduced into the state lation. Observe how the norm off\") evolves over time for the givenA. What do you see happen- to the norm of the state ? the feedback computed in part (c) to the system in the notebook andexplain how the norm of state changes . av we evaluate a system described by the following scalar systemz(t+ 1) = az(t) + u{t) + w(t) in Jupyter notebook. Consider two values ofa, one case with a > 1 and one with a