On the Numerical Solution of Differential Linear Matrix Inequalities

Marco Ariola (), Gianmaria De Tommasi (), Adriano Mele () and Gaetano Tartaglione ()
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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

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 2, No 12, 540-553

Abstract: 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.

Keywords: Differential LMIs; Optimization; Time-varying systems; 93C05; 93B50; 93D05; 93C57 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01650-9

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