Extension of Lossless Negative Imaginary Lemmas to Systems with Poles at the Origin

  • Junlin XiongEmail author
  • Yongge Guo
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 480)


This paper is concerned with extending lossless negative imaginary lemmas to the dynamical system with poles at the origin. Firstly, two versions of lossless negative imaginary lemma are established in terms of a set of linear matrix equations. They can be considered as extensions of the previous results. Secondly, a new type of lossless negative imaginary lemma is derived based on Kalman canonical decomposition of system state-space realization. The second type of lossless negative imaginary lemma does not require solving linear matrix equations, which is more computationally efficient. Finally, the validity of the developed lemmas is illustrated by a numerical example.


Linear systems Lossless negative imaginary systems Kalman decomposition 



The work in this paper was financially supported by National Natural Science Foundation of China (No.61374026, No. 61773357).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of AutomationUniversity of Science and Technology of ChinaHefeiChina

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