Feedback control systems using sensors and actuators such as piezoelectric sensors and actuators, micro-electro-mechanical systems (MEMS) sensors and opto-mechanical sensors, are allowing new advances in designing such high precision technologies. The negative imaginary control systems framework allows for robust control design for such high precision systems in the face of uncertainties due to unmodelled dynamics. The stability of the feedback interconnection of negative imaginary systems has been well established in the literature. However, the proofs of stability feedback interconnection which are used in some previous papers have a shortcoming due to a matrix inevitability issue. In this paper, we provide a new and correct Lyapunov-based proof of one such result and show that the result is still true.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors would like to acknowledge Sei Zhen Khong who originally pointed out to the problem with the proof of Theorem 5 in Xiong et al. . This work was supported by the Australian Research Council under grant DP160101121.