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1
Content available The parametric optimization of a system with two delays and a PI controller
Duda Jozef
Archives of Control Sciences
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2019
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Vol. 29, No. 4
667--686
EN
In the paper a Lyapunov matrices approach to the parametric optimization problem of a time-delay system with two commensurate delays and a PI-controller is presented. The value of integral quadratic performance index is equal to the value of the Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix. In the paper is presented the example of a scalar system with two delays and a PI controller.
2
Content available Robust stabilization using a sampled-data strategy of uncertain neutral state-delayed systems subject to input limitations
El Fezazi N., El Haoussi F., Tissir E. H., Alvarez T., Tadeo F.
International Journal of Applied Mathematics and Computer Science
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2018
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Vol. 28, no. 1
111--122
EN
Stabilization of neutral systems with state delay is considered in the presence of uncertainty and input limitations in magnitude. The proposed solution is based on simultaneously characterizing a set of stabilizing controllers and the associated admissible initial conditions through the use of a free weighting matrix approach. From this mathematical characterization, state feedback gains that ensure a large set of admissible initial conditions are calculated by solving an optimization problem with LMI constraints. Some examples are presented to compare the results with previous approaches in the literature.
3
Content available A Lyapunov functional for a system with both lumped and distributed delay
Duda J.
Archives of Control Sciences
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2017
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Vol. 27, no. 4
527--540
EN
In the paper construction of a Lyapunov functional for time delay system with both lumped and distributed delay is presented. The Lyapunov functional is determined by means of the Lyapunov matrix. The method of determination of the Lyapunov matrix for time delay system with both lumped and distributed delay is presented. It is given the example illustrating the method.
4
Content available Lyapunov Matrices Approach to the Parametric Optimization of a System with Two Delays
Duda J.
Archives of Control Sciences
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2016
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Vol. 26, no. 3
367--381
EN
In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with two commensurate delays and a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of the Lyapunov functional for the initial function of time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix.
5
Content available Lyapunov matrices approach to the parametric optimization of time-delay systems
Duda J.
Archives of Control Sciences
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2015
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Vol. 25, no. 3
279--288
EN
In the paper a Lyapunov matrices approach to the parametric optimization problem of timedelay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix.
6
Content available On dynamical identification of control in a system with time delay
Maksimov V.
Archives of Control Sciences
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2012
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Vol. 22, no. 1
5-15
EN
The problem of identification of a control through results of observations of phase states of dynamical systems described by differential equations with time delay is discussed. The paper presents an algorithm based on the method of feedback control with a model. The algorithm is stable with respect to informational noises and computational errors.
7
Content available remote Persistent bounded disturbance rejection for uncertain time-delay systems
Sun M., Jia Y.
Control and Cybernetics
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2009
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Vol. 38, no 3
593-607
EN
This paper considers the problem of persistent bounded disturbance rejection for a class of time-delay systems with parametric uncertainty by Lyapunov function and positively invariant set analysis method. Sufficient conditions for internal stability and L1-performance analysis are given in terms of linear matrix inequalities (LMIs). Based on the results, a simple approach to the design of a linear state-feedback controller is presented to stabilize robustly the uncertain time-delay systems and achieve a desired level of disturbance attenuation. All the obtained conditions are delay-dependent. A numerical example is included to illustrate the proposed method.
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