A new approach in state feedback controller design of LTI systems with input time delay

This paper investigates the stability analysis and state feedback controller design 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 vectors related to the system parameters and the feedback gain. The characteristic roots can be determined exactly and concisely 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 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.