A bivector rotation approach to state feedback stabilization of linear time-invariant systems with input time delay

This paper investigates the state feedback stabilization of linear time-invariant (LTI) systems with input time delay. By investigating the real part and the imaginary part of the transcendental equation, the characteristic equation can be transformed into an equation with two bivectors related to the system parameters and the feedback gain. Using the bivector rotation principle, the characteristic roots in the imaginary axis can be determined exactly and concisely. This result is novel in that it separates the delay element from the system parameters and the feedback gain so that the feedback gain can be designed directly under a given time delay condition. Based on this approach and the pole placement method, preservation of the closed-loop control performance, the state feedback stabilization gain, and the maximum allowable value of input time delay can be derived by solving an optimization equation. Numerical examples are provided to illustrate the proposed algorithm.