Lyapunov-based Stability of Feedback Interconnections of Negative Imaginary Systems

Ahmed G. Ghallab; Mohamed A. Mabrok; Ian R. Petersen

doi:10.1016/j.ifacol.2017.08.839

Lyapunov-based Stability of Feedback Interconnections of Negative Imaginary Systems

Ahmed G. Ghallab, Mohamed A. Mabrok, Ian R. Petersen

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	3424-3428
Number of pages	5
Journal	IFAC-PapersOnLine
Volume	50
Issue number	1
DOIs	https://doi.org/10.1016/j.ifacol.2017.08.839
Publication status	Published - Jul 2017

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10.1016/j.ifacol.2017.08.839

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abstract = "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.",

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AU - Mabrok, Mohamed A.

AU - Petersen, Ian R.

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AB - 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.

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Lyapunov-based Stability of Feedback Interconnections of Negative Imaginary Systems

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