4. Given the discrete time system $y(k+1) - y(k) = x(k+1)$ find the system transfer function and its response for a sampled unit.
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The following difference equation models a discrete-time control system: y(k+3) - y(k+2) + y(k+1) + 2y(k) = u(k) - y(k+1) - 2y(k+2) where u(k) is the input. Let the output be c(k) = y(k+1). (i) Define state variables and find a state-space representation for the system. (ii) Determine the transfer function C(z)/U(z) where C(z) and U(z) are the Z-transforms of c(k) and u(k), respectively.
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For each k ∈ R, determine the value(s) of k for which the system has no solution? A. k = 1 B. k = -1 C. k = ±1 D. k = 0
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