A LTI system is represented by an ordinary differential equation (a) Obtain the transfer function H(s) =

Question:

A LTI system is represented by an ordinary differential equation

d'y(t) , dy(t) dx(t) — х(t) – 2y(t) = dt dt dt?

(a) Obtain the transfer function H(s) = Y(s)/X(s) = B(s)/A(s) and find its poles and zeros. Is this system BIBO stable? Is there any pole-zero cancelation?

(b) Decompose H(s) as W(s)/X(s) = 1/A(s) and Y(s)/W(s) = B(s) for an auxiliary variable w(t) with W(s) as its Laplace transform. Obtain a state/output realization that uses only two integrators. Call the state variable v₁(t) the output of the first integrator and v₂(t) the output of the second integrator. Give the matrix A₁, and the vectors b₁, and c^T₁ corresponding to this realization.

(d) Use the MATLAB€™s function tf2ss to obtain state and output realization from H(s). Give the matrix A_c€™ and the vectors b_c€™ and c^T_c. How do these compare to the ones obtained before.