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2008•IEEE Transactions on Automatic ControlRequires access

Solution to Generalized Sylvester Matrix Equations

Ai‐Guo Wu, Guang‐Ren Duan, Bin Zhou

Open publisher page 51 citations

Abstract

An explicit solution to the generalized Sylvester matrix equation AX+BY= EXF is established. This solution is expressed in terms of the R-controllability matrix of (E, A, B), a generalized symmetric operator matrix and an observability matrix. Moreover, based on this solution, solutions to some other matrix equations are also derived. The results may provide great convenience for the analysis and synthesis problems related to these equations.

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What this paper is about

An explicit solution to the generalized Sylvester matrix equation AX+BY= EXF is established. This solution is expressed in terms of the R-controllability matrix of (E, A, B), a generalized symmetric operator matrix and an observability matrix. Moreover, based on this solution, solutions to some other matrix equations are also derived. The results may provide great convenience for the analysis and synthesis problems related to these equations.

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OpenAlex reports 51 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

An explicit solution to the generalized Sylvester matrix equation AX+BY= EXF is established. This solution is expressed in terms of the R-controllability matrix of (E, A, B), a generalized symmetric operator matrix and an observability matrix. Moreover, based on this solution, solutions to some other matrix equations are also derived. The results may provide great convenience for the analysis and synthesis problems related to these equations.

Key concepts: Sylvester matrix, Sylvester equation, Sylvester's law of inertia, Observability, Controllability, Mathematics, Matrix (chemical analysis), Matrix function

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