Invariance properties in the root sensitivity of time-delay systems with double imaginary roots

DOI10.1016/j.automatica.2010.03.014zbMath1191.93049OpenAlexW1989251100MaRDI QIDQ976289

Wim Michiels, Elias Jarlebring

Publication date: 17 June 2010

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.automatica.2010.03.014

zbMATH Keywords

sensitivitytime-delay systemsperturbation analysisroot locusdouble rootscritical delaysimaginary axis

Mathematics Subject Classification ID

Perturbations in control/observation systems (93C73) Eigenvalue problems (93B60) Control/observation systems governed by ordinary differential equations (93C15)

Related Items (13)

Convergence factors of Newton methods for nonlinear eigenvalue problems ⋮ Reversals in stability of linear time-delay systems: a finer characterization ⋮ Invariance properties for a class of quasipolynomials ⋮ Analyzing the convergence factor of residual inverse iteration ⋮ Broyden's Method for Nonlinear Eigenproblems ⋮ Asymptotic Analysis of Multiple Characteristics Roots for Quasi-polynomials of Retarded-Type ⋮ Stability of linear time invariant fractional delay systems of retarded type in the space of delay parameters ⋮ Weierstrass Approach to Asymptotic Behavior Characterization of Critical Imaginary Roots for Retarded Differential Equations ⋮ The asymptotic analysis of multiple imaginary characteristic roots for LTI delayed systems based on Puiseux–Newton diagram ⋮ Local convergence of Newton-like methods for degenerate eigenvalues of nonlinear eigenproblems: II. Accelerated algorithms ⋮ Stability analysis of descriptor systems with multiple commensurate time-delays ⋮ Counting characteristic roots of linear delay differential equations. I: Frequency-sweeping stability tests and applications ⋮ A reliable graphical criterion for TDS stability analysis

Cites Work

• A new method for computing delay margins for stability of linear delay systems
• Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations
• Discrete delay, distributed delay and stability switches
• Delay effects on stability. A robust control approach
• Extraction of 3D stability switching hypersurfaces of a time delay system with multiple fixed delays
• Direct method for TDS stability analysis
• Deterministic identification of linear dynamic systems
• An analytic stability test for a class of time-delay systems
• A matrix method for determining the imaginary axis eigenvalues of a delay system
• On the delay sensitivity of Smith Predictors
• Stability of Linear Neutral Time-Delay Systems: Exact Conditions via Matrix Pencil Solutions
• Unnamed Item

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