Parametric optimization of neutral linear system with two delays with P-controller

• Autorzy: Duda J.
• Języki publikacji: EN

Abstrakty

EN

In the paper the problem of parametric optimization of a linear neutral system with two delays accomplished with respect to the integral quadratic performance index is formulated and solved. A method of computing the value of performance index relies on determining such a Lyapunov functional defined on the state space that its value for the initial state is equal to that of performance index. In the paper the form of Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of the theory discussed is presented. It concerns a system with the P-controller designed to control a plant with two delays both retarded and neutral type. For such a system the value of the considered performance index is determined.

Słowa kluczowe

EN

parametric optimization; Lyapunov functional; time delay system; neutral system

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2011
• Tom: Vol. 21, no. 4
• Strony: 363--372
• Opis fizyczny: Bibliogr. 13 poz., wzory

Twórcy

autor

Duda J.

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

Bibliografia

• [1] J. Duda: Parametric optimization problem for systems with time delay. PhD thesis AGH University of Science and Technology, Poland, 1986.
• [2] J. J. Duda: Parametric optimization of neutral linear system with respect to the general quadratic performance index. Archiwum Automatyki i Telemechaniki, former Archives of Control Sciences, 33 (1988), 448-456.
• [3] J. J. Duda: Lyapunov functional for a linear system with two delays. Control and Cybernetics, 39 (2010), 797-809.
• [4] J. J. Duda: Lyapunov functional for a linear system with two delays both retarded and neutral type. Archives of Control Sciences, 20 (2010), 89-98.
• [5] J. J. Duda: Lyapunov functional for a system with k-non-commensurate neutral time delays, Control and Cybernetics, 39 (2010), 1173-1184.
• [6] H. Górecki, S. Fuksa, P. Grabowski and A. Korytowski: Analysis and Synthesis of Time Delay Systems. John Wiley & Sons, Chichester, New York, Brisbane, Toronto, Singapore, (1989).
• [7] E. F. Infante, W. B. Castelan: A Liapunov functional for a matrix difference-differential equation. J. Differential Equations, 29 (1978), 439-451.
• [8] V. L. Kharitonov: Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case. Int. J. of Control, 78 (2005), 783-800.
• [9] V. L. Kharitonov: Lyapunov matrices for a class of neutral type time delay systems. Int. J. of Control, 81 (2008), 883-893.
• [10] V. L. Kharitonov and E. Plischke: Lyapunov matrices for time-delay systems. Systems & Control Letters, 55 (2006), 697-706.
• [11] V. L. Kharitonov, A. P. Zhabko: Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems. Automatica, 39 (2003), 15-20.
• [12] J. J. Klamka: Controllability of Dynamical Systems. Kluwer Academic Publishers Dordrecht (1991).
• [13] Yu. M. Repin: Quadratic Lyapunov functionals for systems with delay. Prikl. Mat. Mekh., 29 (1965), 564-566.