F.A. Aliev and V.B. Larin. Optimization of Linear Control Systems: Analytical Methods and Computational Algorithms, volume 8 of Stability and Control: Theory, Methods and Applications. Gordon and Breach, 1998. Home/Search Document Not in Database Summary Related Articles Check |
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Formal Derivation of Algorithms: The Triangular Sylvester.. - Quintana-Ortí, Geijn (2001) (Correct)
.... of the Sylvester equation and numerical solvers see, e.g. 3, 7, 11] Sylvester equations have numerous applications in control theory, signal processing, ltering, image restoration, the decoupling of ordinary and partial di erential equations, and block diagonalization of matrices; see, e.g. [1, 5, 8, 14]. Also note that B = A T yields the Lyapunov equation such that everything derived here can be used (and simpli ed) for this type of equations playing a vital role in many areas of computer aided control system design. Here we focus on the triangular case of the Sylvester equation where the ....
F.A. Aliev and V.B. Larin. Optimization of Linear Control Systems: Analytical Methods and Computational Algorithms, volume 8 of Stability and Control: Theory, Methods and Applications. Gordon and Breach, 1998.
A Unified Deflating Subspace Approach for Classes of.. - Benner, Byers.. (2000) (Correct)
....Z B 11 Gamma I)A 11 A 21 = 0: 38) The existence of solutions for (38) as well as (37) follows from Corollary 3.1 with the matrices in (36) but with an additional restriction for the nonsingularity of B 11 B 12 Z. Another formulation, using generalized inverses allows to drop this condition [1]. 9 Theorem 4.1 Let A, B, C be as in (36) and let U , V and W be as in (7) satisfying (11) If W 1 and B 11 W 1 B 12 W 2 are invertible, then U 1 and V 1 are invertible and X = U 2 U Gamma1 1 , Y = V 2 V Gamma1 1 and Z = W 2 W Gamma1 1 satisfy (37) and (38) Proof. The proof is ....
F.A. Aliev and V.B. Larin. Optimization of Linear Control Systems: Analytical Methods and Computational Algorithms. Stability and Control: Theory, Methods and Applications. Gordon and Breach, 1998.
A Unified Deflating Subspace Approach for Classes of.. - Benner, Byers.. (2000) (Correct)
....Z B 11 Gamma I)A 11 A 21 = 0: 43) The existence of solutions for (43) as well as (42) follows from Corollary 3.1 with the matrices in (41) but with an additional restriction for the nonsingularity of B 11 B 12 Z. Another formulation, using generalized inverses allows to drop this condition [1]. Theorem 4.1 Let A, B, C be as in (41) and let U , V and W be as in (7) satisfying (11) If W 1 and B 11 W 1 B 12 W 2 are invertible, then U 1 and V 1 are invertible and X = U 2 U Gamma1 1 , Y = V 2 V Gamma1 1 and Z = W 2 W Gamma1 1 satisfy (42) and (43) Proof. The proof is similar ....
F.A. Aliev and V.B. Larin. Optimization of Linear Control Systems: Analytical Methods and Computational Algorithms. Stability and Control: Theory, Methods and Applications. Gordon and Breach, 1998.
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