A Fast Algorithm for State Feedback With the Prescribed Degree of Stability

The present study proposes an iterative algorithm for pole placement within a specified disk for linear continuous‐time systems. Derived from a modified discrete Riccati equation, the algorithm enables automated pole placement within the desired region while ensuring convergence. This study investigates the impact of the proximity of open‐loop poles to the disk boundary on algorithmic efficiency and subsequently outlines strategies for optimizing parameter selection. Furthermore, the algorithm’s inherent convergence towards a single point facilitates the placement of all closed‐loop poles at a common location. Numerical studies demonstrate that the proposed algorithm achieves convergence in as few as n –2 n iterations (where n denotes the system order) when r is chosen sufficiently small to enforce coincident pole placement; for general pole configurations, the iteration count is determined by the parameter choices and can be substantially reduced by applying the selection guidelines established in this paper. The efficacy of this approach is substantiated through a series of illustrative examples.