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Design of Digital State H ∞-Controllers of the MIMO Systems with Prescribed Precision

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Abstract

For the linear MIMO plants subject to polyharmonic perturbations, a method of designing digital state controllers was developed with regard for the requirements on limitedness of the control actions in the stable state as well as on limitedness of the controlled variables. A notion of radius of the stable state of a closed-loop system was introduced, and the problem of using the full state vector to design a discrete controller providing the desired radius was formulated. Its necessary and sufficient solvability conditions were obtained using the procedure of H ∞-optimization by selecting the weight matrices of the discrete Lur’e-Riccati equation.

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REFERENCES

  1. Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A., State-space Solution to Standard H 2 and H ∞ Control Problem, IEEE Trans. Automat. Control, 1989, vol. 34, no.8, pp. 831–846.

    Article  Google Scholar 

  2. Iglesias, P.A. and Glover, K., State-space Discrete-time H ∞ Control Theory, Eur. Control Conf., Grenoble, France, 1991, vol. 2, pp. 1730–1735.

    Google Scholar 

  3. Yaesh, I. and Shaked, U., A Transfer Function Approach to the Problems of Discrete-time Systems: H ∞-optimal Linear Control and Filtering, IEEE Trans. Automat. Control, 1991, vol. 36, no.11, pp. 1264–1271.

    Article  Google Scholar 

  4. Iglesias, P.A. and Glover, K., State-space Approach to Discrete-time H ∞ Control, Int. J. Control, 1991, vol. 54, no.5, pp. 1031–1073.

    Google Scholar 

  5. Gahinet, P. and Apkarian, P., A Linear Matrix Inequality Approach to H ∞ Control, Int. J. Robust Nonlinear Control, 1994, vol. 4, pp. 421–448.

    Google Scholar 

  6. Aleksandrov, A.G. and Chestnov, V.N., Design of MIMO Systems of Predefined Precision. I, Avtom. Telemekh., 1998, no. 7, pp. 83–95.

  7. Aleksandrov, A.G. and Chestnov, V.N., Design of MIMO Systems of Predefined Precision. II, Avtom. Telemekh., 1998, no. 8, pp. 124–138.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    V. N. Chestnov

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  1. V. N. Chestnov
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Translated from Avtomatika i Telemekhanika, No. 8, 2005, pp. 46–51.

Original Russian Text Copyright © 2005 by Chestnov.

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Chestnov, V.N. Design of Digital State H ∞-Controllers of the MIMO Systems with Prescribed Precision. Autom Remote Control 66, 1233–1238 (2005). https://doi.org/10.1007/s10513-005-0164-4

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  • DOI: https://doi.org/10.1007/s10513-005-0164-4

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