Conjectural Approach to Pole Placement

A method for pole assignment is developed following a conjecture arising from the observation of assigning a single pole in the case of a one-state system and/or a single pole for a single input system. the method is first justified for extreme cases, and then proved for the general case. the method does not rely on state transformation; and applies to multi-input systems equally well. the uncontrollable case is also considered, with subsequent simplifying relationships, where in certain cases the matrix inverse involved in computations reduces any left inverse of the input matrix.