Instability conditions for linear time delay systems: a Lyapunov matrix function approach

DOI10.1080/00207179.2011.620632zbMath1236.93136OpenAlexW2151217813MaRDI QIDQ3119113

Blanca Ochoa, Gilberto Ochoa, Sabine Mondié

Publication date: 7 March 2012

Published in: International Journal of Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207179.2011.620632

zbMATH Keywords

instabilitytime delay systemsLyapunov-Krasovskii functional of complete type

Mathematics Subject Classification ID

Linear systems in control theory (93C05) Control/observation systems governed by ordinary differential equations (93C15) Stability of control systems (93D99)

Related Items (14)

Iterative methods for the delay Lyapunov equation with T-Sylvester preconditioning ⋮ Stabilisation of distributed time-delay systems: a smoothed spectral abscissa optimisation approach ⋮ Necessary conditions for the exponential stability of time-delay systems via the Lyapunov delay matrix ⋮ Lyapunov-Krasovskii characterization of the input-to-state stability for neutral systems in Hale's form ⋮ Vladimir Kharitonov: Achievements in research ⋮ Regulation of linear systems with both pointwise and distributed input delays by memoryless feedback ⋮ Necessary conditions of exponential stability for a class of linear neutral-type time-delay systems ⋮ Necessary conditions for exponential stability of linear neutral type systems with multiple time delays ⋮ Estimate of the Exponential Decay of Linear Delay Systems Via the Lyapunov Matrix ⋮ Instability conditions for linear time delay systems: a Lyapunov matrix function approach ⋮ Matrix Polynomials, Similar Operators, and the Imaginary Axis Eigenvalues of a Matrix Delay Equation ⋮ Necessary stability conditions for linear delay systems ⋮ Necessary Stability Conditions for One Delay Systems: A Lyapunov Matrix Approach ⋮ Converse Lyapunov–Krasovskii theorems for systems described by neutral functional differential equations in Hale's form

Cites Work

• Generalization of Liapunov's theorem in a linear delay system
• Lyapunov-Krasovskij approach to the robust stability analysis of time-delay systems
• On delay-dependent stability for linear neutral systems
• Lyapunov matrices for a class of time delay systems
• Sufficient conditions for stability and instability of autonomous functional-differential equations
• Instability conditions for linear time delay systems: a Lyapunov matrix function approach
• Sufficient conditions for instability of delay differential systems
• A matrix method for determining the imaginary axis eigenvalues of a delay system
• A Method and New Results for Stability and Instability of Autonomous Functional Differential Equations

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