Negative Imaginary of Linear Continuous-time Time-delayed Systems

Analysis results based on sufficient convex-optimization are given for negative imaginary of continuous-time linear time-delayed systems. Firstly, definitions on negative imaginary and finite-frequency negative imaginary are introduced based on the counterparts of standard linear systems. By facilitating some frequency analysis techniques and combing some known inequalities, sufficient conditions for checking the negative imaginary and finite-frequency negative imaginary properties are derived, respectively. Based on the results, we can analyze the negative imaginary and finite-frequency negative imaginary properties of linear time-delayed system easily via checking the feasibility of a linear matrix inequality. Finally, numerical examples are given to illustrate the effectiveness of the proposed results.