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LMI based robust state feedback control of negative-imaginary systems

  • Santosh Kumar Choudhary
Article
  • 124 Downloads

Abstract

The importance of robust feedback control for uncertain negative imaginary system lies in its practical relevance and engineering applications, for example, lightly damped flexible structures with collocated position sensors and force actuators. This article investigates an LMI based robust static state internally stabilizing feedback controller of the negative imaginary system in presence of strictly negative imaginary uncertainties. The paper first presents some basic theory of negative imaginary systems and then, a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems. The paper provides a systematic controller synthesis procedure based on negative imaginary lemma to achieve robustness in the feedback control of negative imaginary systems. To show the effectiveness of controller synthesis method, one design example is considered and a static state-feedback controller is constructed to force the plant to be stable. The simulation results of this article demonstrate the usefulness of the design method and we believe that feedback control of the negative imaginary system can benefit control engineering practitioners in a number of ways.

Keywords

Negative imaginary systems Uncertain system State feedback control Positive feedback Robust stability  \(H_{\infty }\) control Lightly damped system 

Notes

Acknowledgments

The author would like to acknowledge the support of Manipal Institute of Technology, Manipal University, Manipal, India

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Instrumentation and Control Engineering, Manipal Institute of TechnologyManipal UniversityManipalIndia

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