All Stabilizing State Feedback Controller for Inverted Pendulum Mechanism

In the literature, finding all stabilizing controllers are widely studied. In this paper, a case study of inverted pendulum is considered to test the methods for finding stabilizing state feedback controller. First, good set of state feedback gain matrix is calculated, two of feedback parameters are fixed to reduce the computational cost. The other two of feedback parameters that make the system stable are then calculated by gridding. The boundary of the stability region is calculated with the frequency method. In order to have fast response, the eigenvalue region of the closed loop system is defined as the left hand side of the -1 + jω line and the stability region for feedback gains are calculated for this scenario.