The resolution of the equation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.gif" display="inline" overflow="scroll"><mml:mi>X</mml:mi><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>X</mml:mi><mml:mi>B</mml:mi><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>H</mml:mi><mml:mi>X</mml:mi></mml:math>and the pole assignment problem: A general approach