Universal Method of Static Output Feedback Pole Placement for Fourth-Order Linear Time-Invariant Systems With Two Inputs and Two Outputs

A universal analytical method of static output feedback pole placement for fourth-order linear time-invariant systems with two control inputs and two observe outputs is suggested, regardless the relations between controllability and observability indices. The method does not require decomposing or reducing a system and may be implied to any fourth-order systems modally controllable by static output feedback, including the systems irreducible to control (observation) with a single input (output). The method is based on linear matrix dependence of a closed-loop control system characteristic polynomial on coefficients and determinant of a matrix of controller by output. The suggesting approach gives the necessary and sufficient condition for static output feedback pole placement - it allows de ning all possible matrices of controllers by output and the conditions of their existence. A new algebraic criterion of complete modal controllability by output is formulated and proved. Examples of the approach application to controlling the aviation and space systems based on linearized models both in numerical and symbolic form are given.