On the Yakubovich frequency theorem for linear non-autonomous control processes

DOI10.3934/dcds.2003.9.677zbMath1028.37014OpenAlexW2024868942MaRDI QIDQ1812323

Roberta Fabbri, Carmen Núñez, Russell A. Johnson

Publication date: 9 September 2003

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2003.9.677

zbMATH Keywords

exponential dichotomiesrotation numbersperiodic control systemsnonautonomous linear differential systemsYakubovich's frequency theorem

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Frequency-response methods in control theory (93C80) Linear-quadratic optimal control problems (49N10) Control problems involving ordinary differential equations (34H05) Ordinary differential equations and systems with randomness (34F05) Topological dynamics of nonautonomous systems (37B55)

Related Items

Null controllable sets and reachable sets for nonautonomous linear control systems, Dynamical methods for linear Hamiltonian systems with applications to control processes, Nonautonomous linear-quadratic dissipative control processes without uniform null controllability, Singular Sturmian comparison theorems for linear Hamiltonian systems, Generalized focal points and local Sturmian theory for linear Hamiltonian systems, Oscillation numbers for continuous Lagrangian paths and Maslov index, Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems, On the solvability of the Yakubovich linear-quadratic infinite horizon minimization problem, Unnamed Item, Focal points and principal solutions of linear Hamiltonian systems revisited, A biography of Russell A. Johnson, Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems, Frequency theorem for parabolic equations and its relation to inertial manifolds theory, Disconjugacy and the rotation number for linear, non-autonomous Hamiltonian systems, Discussion on: ``Delay-dependent \(H_\infty\) control of uncertain discrete delay systems, Non-Atkinson perturbations of nonautonomous linear Hamiltonian systems: exponential dichotomy and nonoscillation, On non-autonomous \(H^{\infty}\) control with infinite horizon, Remarks on linear-quadratic dissipative control systems