Inertia theorems for the periodic Liapunov equation and periodic Riccati equation

DOI10.1016/S0167-6911(84)80048-1zbMath0527.34025MaRDI QIDQ786297

Mark A. Shayman

Publication date: 1984

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

zbMATH Keywords

inertiaRiccati differential equationLyapunov differential equationcharacteristic multipliers

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Matrix equations and identities (15A24) Control problems involving ordinary differential equations (34H05) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Quadratic and bilinear forms, inner products (15A63)

Related Items (7)

Converse Lyapunov functions for exponentially stable periodic orbits ⋮ Nonlinear \(H_{\infty}\) control around periodic orbits ⋮ Riccati differential equation in optimal filtering of periodic non-stabilizable systems ⋮ Stability and inertia ⋮ Optimal control for linear periodic systems by using multirate piecewise constant sampled state feedback ⋮ Inertia theorems for the periodic Lyapunov difference equation and periodic Riccati difference equation ⋮ The extended periodic Lyapunov lemma

Cites Work

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• Some theorems on the inertia of general matrices
• Inertia theorems for matrices, controllability, and linear vibrations
• Controllability and linear closed-loop controls in linear periodic systems
• Second-variation methods in periodic optimization
• A Generalization of a Theorem of Lyapunov
• Existence and uniqueness theorems for the algebraic Riccati equation
• On the algebraic Riccati equation
• Application of Hankel matrix to the root location problem
• Matrix quadratic equations
• A Generalization of the Inertia Theorem

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