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A necessary and sufficient condition in Lyapunov robust control

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Abstract

We consider Lyapunov's equationPA+A T P+Q=0, whereQ is symmetric positive definite andA is in controllable companion form. We prove that a necessary and sufficient condition thatA be stable is that the first rowP 1 of theP-matrix be a stablen−1 coefficient vector. This result is related to the minimum phase property of linear systems and is useful in designing robust controllers.

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Author notes

  1. H. L. Stalford (Associate Professor)

    Present address: School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia

  2. C. H. Chao (Graduate Student)

    Present address: Department of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan 80424, Republic of China

Authors and Affiliations

  1. Interdisciplinary Center of Applied Mathematics and Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

    H. L. Stalford (Associate Professor)

  2. Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

    C. H. Chao (Graduate Student)

Authors
  1. H. L. Stalford
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  2. C. H. Chao
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Communicated by G. Leitmann

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Stalford, H.L., Chao, C.H. A necessary and sufficient condition in Lyapunov robust control. J Optim Theory Appl 63, 191–204 (1989). https://doi.org/10.1007/BF00939573

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