On solving the Lyapunov and Stein equations for a companion matrix |
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Authors: | A. Betser N. Cohen E. Zeheb |
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Abstract: | When the matrix A is in companion form, the essential step in solving the Lyapunov equation PA + ATP = −Q involves a linear n × n system for the first column of the solution matrix P. The complex dependence on the data matrices A and Q renders this system unsuitable for actual computation. In this paper we derive an equivalent system which exhibits simpler dependence on A and Q as well as improved complexity and robustness characteristics. A similar results is obtained also for the Stein equation P − ATPA = Q. |
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Keywords: | Lyapunov equation Stein equation Computational aspects Hurwitz matrix Kronecker products |
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