Lyapunov–Krasovskii approach to the robust stability analysis of time-delay systems

Kharitonov, Vladimir L.; Zhabko, Alexey P.

doi:10.1016/s0005-1098(02)00195-4

Cited by 344 publications

(179 citation statements)

References 4 publications

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“…This value is equal to the value of integral quadratic performance index of quality. In last years a method of determination of the Lyapunov functional by means of Lyapunov matrices is very popular, see for example [5]. In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems is presented.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov matrices approach to the parametric optimization of time-delay systems

Duda¹

2015

Archives of Control Sciences

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Section: Introductionmentioning

confidence: 99%

Lyapunov matrices approach to the parametric optimization of time-delay systems

Duda¹

2015

Archives of Control Sciences

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“…This solution satisfies symmetry and boundary conditions. Kharitonov and Zhabko (2003) extended the results of Infante and Castelan (1978) and proposed a procedure of construction of quadratic functionals for linear retarded type delay systems which could be used for robust stability analysis of time delay systems. This functional was expressed by means of a Lyapunov matrix, which depended on the fundamental matrix of a time delay system.…”

Section: Introductionmentioning

confidence: 77%

A Lyapunov functional for a system with a time-varying delay

Duda¹

2012

International Journal of Applied Mathematics and Computer Science

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“…According to Kharitonov and Zhabko (2003), the matrix U(τ ) associated with W determines the quadratic functional…”

Section: Preliminariesmentioning

confidence: 99%

Synthesis of Razumikhin and Lyapunov–Krasovskii approaches to stability analysis of time-delay systems

Medvedeva

Zhabko

2015

Automatica

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a b s t r a c tIn this paper, a necessary and sufficient condition for the exponential stability of linear systems with several time-delays is presented. Such a condition is based on the construction of quadratic lower bounds for the Lyapunov-Krasovskii functionals on the special Razumikhin-type set of functions. The result reveals a constructive procedure for the stability analysis whose application is illustrated with examples.

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Lyapunov–Krasovskii approach to the robust stability analysis of time-delay systems

Cited by 344 publications

References 4 publications

Lyapunov matrices approach to the parametric optimization of time-delay systems

Lyapunov matrices approach to the parametric optimization of time-delay systems

A Lyapunov functional for a system with a time-varying delay

Synthesis of Razumikhin and Lyapunov–Krasovskii approaches to stability analysis of time-delay systems

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