In a parallel structure of two LTI systems with transfer functions H1(s) and H2(s), the total system transfer function is given by:

Correct option is A

​$$\text{In a parallel interconnection of two LTI systems:} \\[8pt]\bullet \ \text{The same input is applied to both systems.} \\[4pt]\bullet \ \text{The outputs are added to produce the overall output.} \\[8pt]\text{If:} \\[6pt]\bullet \ \text{System 1 has transfer function } H_1(s) \\[2pt]\bullet \ \text{System 2 has transfer function } H_2(s) \\[8pt]\text{Then the total output in the Laplace domain is:} \\[8pt]Y(s) = H_1(s)X(s) + H_2(s)X(s) \\[10pt]\text{Factoring } X(s): \\[8pt]Y(s) = \left[ H_1(s) + H_2(s) \right] X(s) \\[10pt]\text{Hence, the overall transfer function is:} \\[8pt]H(s) = H_1(s) + H_2(s)$$​​