Pole assignment by state-derivative feedback for single-input linear systems

Abstract This paper presents an efficient solution to the pole assignment problem using state-derivative feedback for continuous, single-input, time-invariant, linear systems. This problem is always solvable for any controllable system with some restrictions when assigning zero poles. The proposed solution is based on the transformation to the Hessenberg matrix, which is preferable from the numerical point of view since it may be obtained by orthogonal transformations only. In this work, the non-singular and the singular open-loop state matrices are treated and analytical expressions to the state-derivative feedback gains are introduced. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed solution.