Chain-Scattering Representations of the Plant

Consider a system ∑ of Figure 4.1 with two kinds of inputs (b₁, b₂) and two kinds of outputs (a₁, a₂) represented as 4.1$$\left[ {\begin{array}{*{20}{c}} {{{a}_{1}}} \\ {{{a}_{2}}} \\ \end{array} } \right] = \sum {\left[ {\begin{array}{*{20}{c}} {{{b}_{1}}} \\ {{{b}_{2}}} \\ \end{array} } \right]} = \left[ {\begin{array}{*{20}{c}} {{{\sum }_{{11}}}} & {{{\sum }_{{12}}}} \\ {{{\sum }_{{21}}}} & {{{\sum }_{{22}}}} \\ \end{array} } \right]\left[ {\begin{array}{*{20}{c}} {{{b}_{1}}} \\ {{{b}_{2}}} \\ \end{array} } \right].$$Figure 4.1Input-Output Representation.