Explicit solutions of conjugate, periodic, time-varying Sylvester equations

Li Ma; Rui Chang; Mengqi Han; Yongmei Jiao

doi:10.1186/s13660-023-03048-3

journal article Open Access Oct 19, 2023

Explicit solutions of conjugate, periodic, time-varying Sylvester equations

Li Ma

Rui Chang

Mengqi Han Yongmei Jiao

Journal of Inequalities and Applications Vol. 2023 No. 1 · Springer Science and Business Media LLC

View at Publisher Save 10.1186/s13660-023-03048-3

Abstract

AbstractSolutions of a group of conjugate time-varying matrix equations are discussed in this paper. Through mathematical derivation, the solutions to this group of equations are equivalent to the solutions to a class of conjugate time-invariant matrix equations. Further, the related conditions of solvability are obtained and the general explicit solutions are represented by using quasicontrollability and quasiobservability matrices. A detailed algorithm is presented to make the calculation process clear, and the effectiveness of the algorithm is verified by a concrete example. The proposed algorithm can provide complete solutions to the considered equation in explicit parametric form and its main computation includes solving an ordinary linear algebraic equation and some matrix multiplication operations.

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Published: Oct 19, 2023
Vol/Issue: 2023(1)
License: View

Authors

L

Li Ma

Peking-Yale Joint Center for Plant Molecular Genetics and Agrobiotechnology, College of Life Sciences, and the National Laboratory of Protein Engineering and Plant Genetic Engineering, Peking University, Beijing 100871, China (W.G., Y.-P.S., L.-G.M., Y.P., Y.-L.D., D.-H.W., C.-X.D., Y.-H.C., X.-Y.Y., Y.G., D.Z., Y.L., H.-Y.G., L.-J.Q., S.-N.B., J.-D.Z., Y.-X.Z.); State Key Laboratory of Genetic E

Funding

Excellent Youth Fund of Henan Natural Science Foundation Award: 212300410058

Science and Technology Innovation Team Funding of Colleges and Universities in Henan Province Award: 22IRTSTHN011

Cite This Article

Li Ma, Rui Chang, Mengqi Han, et al. (2023). Explicit solutions of conjugate, periodic, time-varying Sylvester equations. Journal of Inequalities and Applications, 2023(1). https://doi.org/10.1186/s13660-023-03048-3

Explicit solutions of conjugate, periodic, time-varying Sylvester equations

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