The Lyapunov matric equation SA+A*S=S*B*BS

DOI10.1016/0024-3795(79)90117-4zbMath0422.15010OpenAlexW2028692229MaRDI QIDQ1133600

David H. Carlson, Biswa Nath Datta

Publication date: 1979

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(79)90117-4

zbMATH Keywords

controllabilityHermitian matriceseigenspacesLyapunov matrix equationD-stable matrices

Mathematics Subject Classification ID

Controllability (93B05) Determinants, permanents, traces, other special matrix functions (15A15) Matrix equations and identities (15A24) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (12)

The matrix equation \(XA-BX=R\) and its applications ⋮ The explicit solution of the matrix equation \(AX-XB = C\) ⋮ Controllability and the linear equation Ax=b ⋮ Controllability, observability and the solution of AX-XB=C ⋮ Some open problems in matrix theory arising in linear systems and control ⋮ On the Controllability of Matrix Pairs $(A,K)$ with K Positive Semidefinite ⋮ Existence condition of positive-definite solutions for algebraic matrix Riccati equations ⋮ The Bezoutian and the eigenvalue-separation problem for matrix polynomials ⋮ Controllability, inertia, and stability for tridiagonal matrices ⋮ Stability and controllability ⋮ Generalized controllability and inertia theory. II ⋮ Linear and numerical linear algebra in control theory: Some research problems

Cites Work

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• Some theorems on the inertia of general matrices
• An inertia theorem for tridiagonal matrices and a criterion of Wall on continued fractions
• Nonsingular solutions of TA-BT=C
• Stability and D-stability
• On the effective computation of the inertia of a non-hermitian matrix
• On ranges of Lyapunov transformations
• Inertia theorems for matrices, controllability, and linear vibrations
• A remark on a theorem of Lyapunov
• Inertia theorems for matrices: the semidefinite case
• A Generalization of a Theorem of Lyapunov
• LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL
• A Generalization of the Inertia Theorem

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