On cones and stability

DOI10.1016/S0024-3795(97)10020-9zbMath0946.15012MaRDI QIDQ1307206

Daniel Hershkowitz

Publication date: 12 October 2000

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

zbMATH Keywords

Lyapunov stabilitymatrix cones

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Stability of solutions to ordinary differential equations (34D20) Positive matrices and their generalizations; cones of matrices (15B48) Linear ordinary differential equations and systems (34A30)

Related Items (12)

A Hill-Pick matrix criterion for the Lyapunov order ⋮ On the Kalman-Yacubovich-Popov Lemma and common Lyapunov solutions for matrices with regular inertia ⋮ On the stability of nonsunspot equilibria ⋮ Multivariate supOU processes ⋮ Strong stability of discrete-time systems ⋮ The distance to strong stability ⋮ Strong stability of internal system descriptions ⋮ Non-overshooting stabilisation via state and output feedback ⋮ The Lyapunov order for real matrices ⋮ A characterization of convex cones of matrices with constant regular inertia ⋮ A pair of matrices sharing common Lyapunov solutions--A closer look ⋮ Singularity conditions for the non-existence of a common quadratic Lyapunov function for pairs of third order linear time invariant dynamic systems

Cites Work

• Unnamed Item
• On the uniqueness of the Lyapunov scaling factors
• A necessary and sufficient condition for the stability of convex combinations of stable polynomials or matrices
• More on the uniqueness of the Lyapunov scaling factors
• Maximal unidirectional perturbation bounds for stability of polynomials and matrices
• Some theorems on the inertia of general matrices
• Block diagonal semistability factors and Lyapunov semistability of block triangular matrices
• Three types of matrix stability
• Classes of stable and semipositive matrices
• Inertia theorems for matrices: the semidefinite case
• On the Inertia of Intervals of Matrices
• Scalings of vector spaces and the uniqueness of lyapunov scaling factors
• Cones of real positive semidefinite matrices associated with matrix stability
• Positive diagonal solutions to the Lyapunov equations
• Theorems of the Alternative for Cones and Lyapunov Regularity of Matrices
• Convex invertible cones and the Lyapunov equation

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