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On the Numerical Solution of Differential Linear Matrix Inequalities

Author

Listed:
  • Marco Ariola

    (Università degli Studi di Napoli Parthenope, Centro Direzionale di Napoli)

  • Gianmaria De Tommasi

    (Università degli Studi di Napoli Federico II)

  • Adriano Mele

    (l’Automazione e le Tecnologie dell’Elettromagnetismo)

  • Gaetano Tartaglione

    (Università degli Studi di Napoli Parthenope, Centro Direzionale di Napoli)

Abstract

This paper presents a novel approach for the numerical solution of differential linear matrix inequalities. The solutions are searched in the class of piecewise-quadratic functions with symmetric matrix coefficients to be determined. To limit the numbers of unknowns, congruence constraints are considered to guarantee continuity of the solution and of its derivative. In Example section, some control problems involving differential linear matrix inequalities are considered and solved in order to compare the proposed approach with alternative approximation methods adopted in the literature.

Suggested Citation

  • Marco Ariola & Gianmaria De Tommasi & Adriano Mele & Gaetano Tartaglione, 2020. "On the Numerical Solution of Differential Linear Matrix Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 540-553, May.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:2:d:10.1007_s10957-020-01650-9
    DOI: 10.1007/s10957-020-01650-9
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