Displaying similar documents to “Stability and stabilization of one class of three time-scale systems with delays”

Observer based control for strong practical stabilization of a class of uncertain time delay systems

Echi Nadhem, Amel Benabdallah (2019)

Kybernetika

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In this paper, we address the strong practical stabilization problem for a class of uncertain time delay systems with a nominal part written in triangular form. We propose, firstly, a strong practical observer. Then, we show that strong practical stability of the closed loop system with a linear, parameter dependent, state feedback is achieved. Finally, a separation principle is established, that is, we implement the control law with estimate states given by the strong practical observer...

On stability of linear neutral differential equations with variable delays

Leonid Berezansky, Elena Braverman (2019)

Czechoslovak Mathematical Journal

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We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays x ˙ ( t ) - a ( t ) x ˙ ( g ( t ) ) + b ( t ) x ( h ( t ) ) = 0 , where | a ( t ) | < 1 , b ( t ) ≥ 0 , h ( t ) ≤ t , g ( t ) ≤ t , and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.

Exponential stability via aperiodically intermittent control of complex-variable time delayed chaotic systems

Song Zheng (2020)

Kybernetika

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This paper focuses on the problem of exponential stability analysis of uncertain complex-variable time delayed chaotic systems, where the parameters perturbation are bounded assumed. The aperiodically intermittent control strategy is proposed to stabilize the complex-variable delayed systems. By taking the advantage of Lyapunov method in complex field and utilizing inequality technology, some sufficient conditions are derived to ensure the stability of uncertain complex-variable delayed...

Growth conditions for the stability of a class of time-varying perturbed singular systems

Faten Ezzine, Mohamed Ali Hammami (2022)

Kybernetika

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In this paper, we investigate the problem of stability of linear time-varying singular systems, which are transferable into a standard canonical form. Sufficient conditions on exponential stability and practical exponential stability of solutions of linear perturbed singular systems are obtained based on generalized Gronwall inequalities and Lyapunov techniques. Moreover, we study the problem of stability and stabilization for some classes of singular systems. Finally, we present a numerical...

On exponential stability of second order delay differential equations

Ravi P. Agarwal, Alexander Domoshnitsky, Abraham Maghakyan (2015)

Czechoslovak Mathematical Journal

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We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones....

Delay-dependent robust stability conditions and decay estimates for systems with input delays

Kostas Hrissagis, Olga I. Kosmidou (1998)

Kybernetika

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The robust stabilization of uncertain systems with delays in the manipulated variables is considered in this paper. Sufficient conditions are derived that guarantee closed-loop stability under state-feedback control in the presence of nonlinear and/or time-varying perturbations. The stability conditions are given in terms of scalar inequalities and do not require the solution of Lyapunov or Riccati equations. Instead, induced norms and matrix measures are used to yield some easy to test...

An analysis on the stability of a state dependent delay differential equation

Sertaç Erman, Ali Demir (2016)

Open Mathematics

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In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term [...] τ(u(t))=a+bu(t)c+bu(t). τ ( u ( t ) ) = a + b u ( t ) c + b u ( t ) . Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.