A two-variable approach to solve the polynomial Lyapunov equation

A two-variable polynomial approach to solve the one-variable polynomial Lyapunov equation is put forward. Such an approach yields an iterative solution method based on the method of Faddeev for the computation of matrix resolvents. The resulting algorithm is especially suitable for applications requiring symbolic or exact computation.

[1]  Bernard Hanzon,et al.  Symbolic computation of Fisher information matrices for parametrized state-space systems , 1999, Autom..

[2]  Ralf Peeters,et al.  A Faddeev sequence method for solving Lyapunov and Sylvester equations , 1996 .

[3]  Ralf Peeters,et al.  A two-variable approach to solve the polynomial Lyapunov equation , 2001 .

[4]  Vladimír Kucera,et al.  Efficient algorithm for matrix spectral factorization , 1985, Autom..

[5]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[6]  P. Fuhrmann.  A Polynomial Approach to Linear Algebra , 1996 .

[7]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[8]  Thomas Kailath,et al.  Linear Systems , 1980 .

[9]  Harry L. Trentelman,et al.  New Algorithms for Polynomial J-Spectral Factorization , 1999, Math. Control. Signals Syst..

[10]  J. Leigh.  LINEAR SYSTEMS AND OPERATORS IN HILBERT SPACE , 1982 .

[11]  R. Kálmán.  Algebraic characterization of polynomials whose zeros lie in certain algebraic domains. , 1969, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Harry L. Trentelman,et al.  On quadratic differential forms , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[13]  A. Talbot,et al.  THE EVALUATION OF INTEGRALS OF PRODUCTS OF LINEAR SYSTEM RESPONSES PART I , 1959 .

[14]  P. Fuhrmann.  Linear Systems and Operators in Hilbert Space , 1982 .

[15]  P. Rapisarda,et al.  A new algorithm to solve the polynomial Lyapunov equation , 2000 .

[16]  J. Jeek,et al.  Paper: Efficient algorithm for matrix spectral factorization , 1985 .

[17]  J. Willems,et al.  On Quadratic Differential Forms , 1998 .

[18]  J. Willems,et al.  Stability theory for high order equations , 1992 .

[19]  B. Hanzon.  Some new results on and applications of an algorithm of Agashe , 1987 .