Inertia theorems for operator Lyapunov inequalities

DOI10.1016/S0167-6911(01)00083-4zbMath0974.93026WikidataQ126759328 ScholiaQ126759328MaRDI QIDQ5941038

Amol J. Sasane, Ruth F. Curtain

Publication date: 20 August 2001

Published in: Systems \& Control Letters (Search for Journal in Brave)

zbMATH Keywords

admissible observation operatorsindefinite inner product spacesinertia theoremsLyapunov equationsspectrum decomposition assumption

Mathematics Subject Classification ID

Eigenvalue problems (93B60) Linear operator inequalities (47A63) Operator-theoretic methods (93B28)

Related Items (5)

Semistability theory for spatially distributed systems ⋮ Optimal Hankel norm approximation for the Pritchard-Salamon class of infinite-dimensional systems ⋮ Sub-optimal Hankel norm approximation for the analytic class of infinite-dimensional systems ⋮ Unnamed Item ⋮ An estimate for the number of eigenvalues of a Hilbert-Schmidt operator in a half-plane

Cites Work

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• Admissible observation operators for linear semigroups
• Inertia and controllability in infinite dimensions
• Some theorems on the inertia of general matrices
• Inertia theorems for matrices, controllability, and linear vibrations
• An inertia theory for operators on a Hilbert space
• New results on the operator Carleson measure criterion
• Conditions for the equivalence of internal and external stability for distributed parameter systems
• All optimal Hankel-norm approximations of linear multivariable systems and theirL,^∞-error bounds†
• Lyapunov and Riccati equations: Periodic inertia theorems
• On the Spectral-Lyapunov Approach to Parametric Optimization of Distributed-Parameter Systems

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