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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
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