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Probability-one homotopy algorithms for solving the coupled Lyapunov equations arising in reduced-order \(H^2/H^\infty\) modeling, estimation, and control. (English) Zbl 1028.93011
The paper deals with the application of homotopy methods for solving a system of coupled matrix Lyapunov equations arising in \(H^2\) and \(H^2/H^\infty\) model reduction and synthesis. Under the requirements of transversality and boundedness of the corresponding homotopy map, a global convergence of probability-one homotopy schemes is analysed.

MSC:
93B40 Computational methods in systems theory (MSC2010)
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
93B36 \(H^\infty\)-control
15A24 Matrix equations and identities
93B11 System structure simplification
93B50 Synthesis problems
Software:
HOMPACK
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References:
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