A negative-imaginary lemma without minimality assumptions and robust state-feedback synthesis for uncertain negative-imaginary systems

作者：Song, Zhuoyue^*; Lanzon, Alexander; Patra, Sourav; Petersen, Ian R.

来源：Systems & Control Letters, 2012, 61(12): 1269-1276.

DOI：10.1016/j.sysconle.2012.08.002

• Negative-imaginary systems
• Lightly damped systems
• Robust control
• Passivity

Negative-imaginary systems have important engineering applications, for example, in lightly damped flexible structures with collocated position sensors and force actuators. This paper proposes a new Negative-Imaginary Lemma for generalized negative-imaginary systems, where the minimality assumption is relaxed. The proposed lemma facilitates both analysis and synthesis for negative-imaginary systems. Invoking this result, a systematic robust static state-feedback synthesis method is proposed in an LMI framework for systems with strictly negative-imaginary uncertainty (e.g. unmodeled spill-over dynamics in a lightly damped flexible structure) assuming all states are available for state feedback. Two numerical examples are given to show the usefulness of the proposed results.

• 出版日期2012-12
• 单位北京理工大学