An LMI approach to discrete-time observer design with stochastic resilience

  • Authors:

  • Edwin Engin Yaz;Chung Seop Jeong;Yvonne Ilke Yaz

  • Affiliations:

  • Department of Electrical and Computer Engineering, Marquette University, Milwaukee, Wisconsin 53210, USA;Department of Electrical and Computer Engineering, Marquette University, Milwaukee, Wisconsin 53210, USA;Milwaukee School of Engineering, Department of Mathematics, Milwaukee, Wisconsin 53202, USA

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2006

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Abstract

Much of the recent work on robust control or observer design has focused on preservation of stability of the controlled system or the convergence of the observer in the presence of parameter perturbations in the plant or the measurement model. The present work addresses the important problem of stochastic resilience or non-fragility of a discrete-time Luenberger observer which is the maintenance of convergence and/or performance when the observer is erroneously implemented possibly due to computational errors i.e. round off errors in digital implementation or sensor errors, etc. A common linear matrix inequality framework is presented to address the stochastic resilient design problem for various performance criteria in the implementation based on the knowledge of an upper bound on the variance of the random error in the observer gain. Present results are compared to earlier designs for stochastic robustness. Illustrative examples are given to complement the theoretical results.