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Extensions in model-based system analysis

  • Author(s): Graham, Matthew R.;
  • et al.

Model-based system analysis techniques provide a means for determining desired system performance prior to actual implementation. In addition to specifying desired performance, model-based analysis techniques require mathematical descriptions that characterize relevant behavior of the system. The developments of this dissertation give ex. tended formulations for control- relevant model estimation as well as model-based analysis conditions for performance requirements specified as frequency domain inequalities. A model estimation algorithm is proposed on the basis of identifying approximately normalized coprime factorizations from closed-loop system input-output measurements. In the proposed method a particular model structure is chosen such that a linear regression in the measurement data is formed, thus sanctioning the use of numerically efficient algorithms in computing the parameter estimates. Furthermore, methods based on closed-loop experimental data support model estimates that are accurate in the frequency region relevant for control design. Specifications for performance and robustness of dynamical systems are commonly expressed in terms of frequency domain inequalities, which due to infinite dimensionality are not directly tractable for analysis and design. A pair of linear matrix inequality conditions are proposed that relate to checking frequency domain inequalities over finite frequency intervals. The proposed conditions introduce an alternative formulation of the Kalman- Yakubovich-Popov Lemma in that the proposed conditions encompasses the lemma for the case when the coefficient matrix of the frequency domain inequality does not depend on frequency. Furthermore, the coefficient matrix can be made affine on the frequency variable at no extra computational cost, which can be significant in reducing conservatism in applications such as robustness analysis. Extensions for the proposed conditions are developed via transformations on the frequency variable. The extensions have many applications including positivity analysis for matrix polynomials, robustness analysis of discrete-time linear systems, as well as analysis conditions on finite frequency intervals that transform to infinite intervals. Application of the alternative conditions and extensions are illustrated with numerical examples in the analysis of robustness

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