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Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis

Author

Listed:
  • Bankmann, Daniel
  • Mehrmann, Volker
  • Nesterov, Yurii

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Van Dooren, Paul

    (Université catholique de Louvain)

Abstract

In this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equations, and their properties are analyzed for continuous- and discrete-time systems. Numerical methods are derived to solve these equations via steepest descent and Newton methods. It is also shown that the analytic center has nice robust- ness properties when it is used to represent passive systems. The results are illustrated by numerical examples.

Suggested Citation

  • Bankmann, Daniel & Mehrmann, Volker & Nesterov, Yurii & Van Dooren, Paul, 2021. "Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis," LIDAM Reprints CORE 3175, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3175
    DOI: https://doi.org/10.1007/s10013-020-00427-x
    Note: In: Vietnam Journal of Mathematics, 2020, vol. 48(4), p. 633-659
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