Lyapunov matrices approach to the parametric optimization of a system with two delays and a PD-controller

• Autorzy: Duda J.

Identyfikatory

DOI

10.24425/acs.2018.125484

• Języki publikacji: EN

Abstrakty

EN

In the paper the parametric optimization problem for a linear system with two delays and a PD-controller is presented. In the parametric optimization problem the quadratic performance index is considered. The value of the quadratic index of quality is calculated due to the Lyapunov functional and is equal to the value of that functional for the initial function of the neutral system with two delays. The Lyapunov functional is determined by means of the Lyapunov matrix.

Słowa kluczowe

EN

neutral system; Lyapunov matrix; Lyapunov functional

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2018
• Tom: Vol. 28, No. 4
• Strony: 585--600
• Opis fizyczny: Bibliogr. 14 poz., tab., wykr., wzory

Twórcy

autor

Duda J.

• AGH University of Science and Technology, Department of Automatic Control and Robotics, Krakow, Poland

Bibliografia

• [1] J. Duda: A Lyapunov functional for a neutral system with a time-varying delay, Bulletin of the Polish Academy of Sciences Technical Sciences, 61 (2013), 911-918.
• [2] J. Duda: Lyapunov matrices approach to the parametric optimization of time-delay systems, Archives of Control Sciences, 25 (2015), 279-288.
• [3] J. Duda: A Lyapunov functional for a neutral system with a distributed time delay, Mathematics and Computers in Simulation, 119 (2016), 171-181.
• [4] J. Duda: Lyapunov matrices approach to the parametric optimization of a neutral system, Archives of Control Sciences, 26 (2016), 81-93.
• [5] J. Duda: Lyapunov matrices approach to the parametric optimization of a system with two delays, Archives of Control Sciences, 26 (2016), 281-295.
• [6] J. Duda: Lyapunov matrices approach to the parametric optimization of a neutral system with two delays,Mathematics and Computers in Simulation, 136 (2017), 22-35.
• [7] H. Gorecki, S. Fuksa, P. Grabowski, and A. Korytowski: Analysis and Synthesis of Time Delay Systems, John Wiley & Sons, Chichester, New York, Brisbane, Toronto, Singapore 1989.
• [8] V. L. Kharitonov: Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case, International Journal of Control, 78 (2005), 783-800.
• [9] V. L. Kharitonov: Lyapunov matrices for a class of neutral type time delay systems, International Journal of Control, 81 (2008), 883-893.
• [10] V. L. Kharitonov: On the uniqueness of Lyapunov matrices for a time-delay system, Systems & Control Letters, 61 (2012), 397-402.
• [11] V. L. Kharitonov and E. Plischke: Lyapunov matrices for time-delay systems, Systems & Control Letters, 55 (2006), 697-706.
• [12] Yu. M. Repin: Quadratic Lyapunov functionals for systems with delay, Prikladnaya Matematika i Mekhanika, 29 (1965), 564-566.
• [13] S. Rodriguez, V. L. Kharitonov, J. Dion, and L. Dugard: Robust stability of neutral systems: a Lyapunov-Krasovskii constructive approach, International Journal of Robust and Nonlinear Control, 14 (2004), 1345-1358.
• [14] J. E. Velazquez-Velazquez and V. L. Kharitonov: Lyapunov-Krasovskii functionals for scalar neutral type time delay equations, Systems & Control Letters, 58 (2009), 17-25.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).