A parametric approach of partial eigenstructure assignment for high-order linear systems via proportional plus derivative state feedback

Abstract

In this paper, a partial eigenstructure assignment problem for the high-order linear time-invariant (LTI) systems via proportional plus derivative (PD) state feedback is considered. By partitioning the open-loop system into two parts (the altered part and the unchanged part) and utilizing the solutions to the high-order generalized Sylvester equation (HGSE), complete parametric expressions of the feedback gain matrices of the closed-loop system are established. Meanwhile, a group of arbitrary parameters representing the degrees of freedom of the proposed method is provided and optimized to satisfy the stability of the system and robustness criteria. Finally, a numerical example and a three-axis dynamic flight motion simulator system example with the simulation results are offered to illustrate the effectiveness and superiority of the proposed method.

Keywords

• partial eigenstructure assignment
• high-order lti systems
• parametric approach
• high-order generalized sylvester equations (hgse)
• pd state feedback