For each of the systems of Problem, determine(a) stability (use MATLAB as required)(b) the...

For each of the systems of Problem, determine

(a) stability (use MATLAB as required)

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(b) the system modes

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(c) the inverse system’s transfer function

Consider the LTI systems described by the following differential equations.

(i)

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(ii)

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(iii)

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(iv)

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(v)

(a) Find the unit impulse response h(t) for each system.

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(b) Verify all partial-fraction expansions using MATLAB.

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(c) Find the unit step response s(t) for each system.

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(d) To verify your results, show that the functions in Parts (a) and (c) satisfy the equation

relating the impulse response h(t) and the step response s(t).