A state space system is defined as

\(\mathop X\limits^ .\) = \(AX + BU\)

\(Y = CX + DU\)

Transfer function of the system is

\(G\left( S \right) = {{{K_1}} \over {s + 3}} + {{{K_2}} \over {s + 4}} + {{{K_3}} \over {s + 5}}\)

If \(C=[K_1 K_2 K_3 ]\) and \(D = \left[ 0 \right]\) then A and B are respectively:

\(A = \left[ {\matrix{ 0 & 0 & 1 \cr 0 & 1 & 0 \cr { - 3} & { - 4} & { - 5} \cr } } \right],B = \left[ {\matrix{ 0 \cr 0 \cr 1 \cr } } \right]\)

\(A = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr { - 5} & { - 4} & { - 3} \cr } } \right],B = \left[ {\matrix{ 0 \cr 0 \cr 0 \cr } } \right]\)

\(A = \left[ {\matrix{ { - 3} & 0 & 0 \cr 0 & { - 4} & 0 \cr 0 & 0 & { - 5} \cr } } \right],B = \left[ {\matrix{ 0 \cr 0 \cr 1 \cr } } \right]\)

\(A = \left[ {\matrix{ { - 3} & 0 & 0 \cr 0 & { - 4} & 0 \cr 0 & 0 & { - 5} \cr } } \right],B = \left[ {\matrix{ 1 \cr 1 \cr 1 \cr } } \right]\)