Robust controlled positive delayed systems with interval parameter uncertainties: A delay uniform decomposition approach

• Autorzy: Elloumi W. , Mehdi D. , Chaabane M.

Identyfikatory

DOI

10.2478/amcs-2018-0033

• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with robust stabilization of continuous linear positive time-delay systems with parametric uncertainties. The delay considered in this work is a bounded time-varying function. Previously, we have demonstrated that the equidistant delay-decomposition technique is less conservative when it is applied to linear positive time-delay systems. Thus, we use simply a delay bi-decomposition in an appropriate Lyapunov–Krasovskii functional. By using classical and partitioned control gains, the state-feedback controllers developed in our work are formulated in terms of linear matrix inequalities. The efficiency of the proposed robust control laws is illustrated with via an example.

Słowa kluczowe

EN

delay system; robust stabilization; positive system; parametric constraints; delay decomposition; LMIs

PL

układ z opóźnieniem; stabilizacja odporna; układ dodatni; ograniczenia parametryczne; LMIs

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2018
• Tom: Vol. 28, no. 3
• Strony: 441--450
• Opis fizyczny: Bibliogr. 22 poz., tab., wykr.

Twórcy

autor

Elloumi W.

• Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), University of Sfax, PB 1173, 3038 Sfax, Tunisia

autor

Mehdi D.

• Laboratory of Computer Science and Automatic Control for Systems (LIAS/ENSIP), University of Poitiers, 2, rue Pierre Brousse, 86073 Poitiers Cedex 9, France

autor

Chaabane M.

• Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), University of Sfax, PB 1173, 3038 Sfax, Tunisia

Bibliografia

• [1] Araki, M. (1975). Application of m-matrices to the stability problems of composite dynamical systems, Journal of Mathematical Analysis and Applications 52(2): 309–321.
• [2] Bolajraf, M. (2012). Robust Control and Estimation for Positive Systems, Valladolid University, Valladolid.
• [3] Chen, X., Chen, M. and Shen, J. (2017). A novel approach to l1-induced controller synthesis for positive systems with interval uncertainties, Journal of The Franklin Institute 354(8): 3364–3377.
• [4] Elloumi, W., Mehdi, D., Chaabane, M. and Hashim, G. (2015). Exponential stability criteria for positive systems with time-varying delay: A delay decomposition technique, Circuits, Systems and Signal Processing 35(5): 1545–1561.
• [5] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, Wiley, New York, NY.
• [6] Hale, J. and Lunel, S.M.V. (1993). Introduction to Functional Differential Equations, Springer, New York, NY.
• [7] Hmamed, A., Rami, M.A., Benzaouia, A. and Tadeo, F. (2012). Stabilization under constrained states and controls of positive systems with time delays, Mechanical Systems and Signal Processing 18(2): 182–190.
• [8] Junfeng, Z., Xianglei, J., Ridong, Z. and Shizhou, F. (2017). Parameter-dependent Lyapunov function based model predictive control for positive systems and its application in urban water management, Control Conference (CCC), Dalian, China.
• [9] Kaczorek, T. (2014). Minimum energy control of fractional positive continuous-time linear systems with bounded inputs, International Journal of Applied Mathematics and Computer Science 24(2): 335–340, DOI: 10.2478/amcs-2014-0025.
• [10] Kaczorek, T. (2016). Positivity and stability of fractional descriptor time-varying discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 26(1): 5–13, DOI: 10.1515/amcs-2016-0001.
• [11] Luenberger, D.G. (1976). Introduction to Dynamic Systems: Theory, Models and Applications, Academic Press, New York, NY.
• [12] Mesquine, F., Hmamed, A., Benhayoun, M., Benzaouiaa, A. and Tadeo, F. (2015). Robust stabilization of constrained uncertain continuous-time fractional positive systems, Journal of The Franklin Institute 352(1): 259–270.
• [13] Rami, M.A. (2011). Solvability of static output-feedback stabilization for LTI positive systems, Systems & Control Letters 60(9): 704–708.
• [14] Rami, M.A., Tadeo, F. and Benzaouia, A. (2007). Control of constrained positive discrete systems, Proceedings of the American Control Conference, New York, NY, USA, pp. 5851–5856.
• [15] Shorten, R., Wirth, F. and Leith, D. (2006). A positive systems model of TCP-like congestion control: Asymptotic results, IEEE Transactions on Networking 14(2): 616–629.
• [16] Shuqian, Z., Han, Q.-L. and Zhang, C. (2014). l1-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: A linear programming approach, Automatica 50(8): 2098–2107.
• [17] Zaidi, I. (2015). Robust Stabilization and Observation for Positive Takagi–Sugeno systems, PhD thesis, Valladolid University, Valladolid.
• [18] Zaidi, I., Chaabane, M., Tadeo, F. and Benzaouia, A. (2014). Static state feedback controller and observer design for interval positive systems with time-delay, IEEE Transactions on Circuits and Systems II 62(5): 506–510.
• [19] Zhang, Z. and Yang, H. (2013). Stability and Hopf bifurcation in a three-species food chain system with harvesting and two delays, Journal of Computational and Nonlinear Dynamics 9(2), Paper no.: CND-12-1233.
• [20] Zhu, S., Han, Q.-L. and Zhang, C. (2016). Investigating the effects of time-delays on stochastic stability and designing l1-gain controllers for positive discrete-time Markov jump linear systems with time-delay, Information Sciences 355(C): 265–281.
• [21] Zhu, S., Han, Q.-L. and Zhang, C. (2017). l1-Stochastic stability and l1-gain performance of positive Markov jump linear systems with time-delays: Necessary and sufficient conditions, IEEE Transactions on Automatic Control 62(7): 3634–3639.
• [22] Zhu, S., Meng, M. and Zhang, C. (2013). Exponential stability for positive systems with bounded time-varying delays and static output feedback stabilization, Journal of The Franklin Institute 350(3): 617–636.

Uwagi

PL

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