Displaying similar documents to “Estimation for linear pure delay time systems”

Characterization of shadowing for linear autonomous delay differential equations

Mihály Pituk, John Ioannis Stavroulakis (2025)

Czechoslovak Mathematical Journal

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A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear autonomous delay differential equation is shadowable if and only if its characteristic equation has no root on the imaginary axis. The proof is based on the decomposition theory of linear delay differential equations.

Oscillation of delay differential equations

J. Džurina (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0.

Finite-time outer synchronization between two complex dynamical networks with time delay and noise perturbation

Zhi-cai Ma, Yong-zheng Sun, Hong-jun Shi (2016)

Kybernetika

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In this paper, the finite-time stochastic outer synchronization and generalized outer synchronization between two complex dynamic networks with time delay and noise perturbation are studied. Based on the finite-time stability theory, sufficient conditions for the finite-time outer synchronization are obtained. Numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of time delay and noise perturbation on the convergence time are also numerically...

Delay differential systems with time-varying delay: new directions for stability theory

James Louisell (2001)

Kybernetika

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In this paper we give an example of Markus–Yamabe instability in a constant coefficient delay differential equation with time-varying delay. For all values of the range of the delay function, the characteristic function of the associated autonomous delay equation is exponentially stable. Still, the fundamental solution of the time-varying system is unbounded. We also present a modified example having absolutely continuous delay function, easily calculating the average variation of the...

Delay-dependent asymptotic stabilitzation for uncertain time-delay systems with saturating actuators

Pin-Lin Liu (2005)

International Journal of Applied Mathematics and Computer Science

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This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.

Time-varying time-delay estimation for nonlinear systems using neural networks

Yonghong Tan (2004)

International Journal of Applied Mathematics and Computer Science

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Nonlinear dynamic processes with time-varying time delays can often be encountered in industry. Time-delay estimation for nonlinear dynamic systems with time-varying time delays is an important issue for system identification. In order to estimate the dynamics of a process, a dynamic neural network with an external recurrent structure is applied in the modeling procedure. In the case where a delay is time varying, a useful way is to develop on-line time-delay estimation mechanisms to...