A generalized approach to stabilization of linear interconnected time-delay systems. (English) Zbl 1303.93142
Summary: The objective of this paper is to propose a generalized approach to stabilization of systems which are composed of linear time-delay subsystems coupled by linear time-varying interconnections. The proposed algorithms, which are formulated within the convex optimization framework, provide decentralized solutions to the problem of delay-dependent asymptotic stability with strict dissipativity. It is established that the new methodology can reproduce earlier results on passivity, positive realness and disturbance attenuation. Then a decentralized structure of dissipative state-feedback controllers is designed to render the closed-loop interconnected system delay-dependent asymptotically stable with strict dissipativity. Numerical examples are presented to illustrate the applicability of the design method.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93A14 | Decentralized systems |
| 93C05 | Linear systems in control theory |
Keywords:
dissipativity; interconnected time-delay systems; delay-dependent stability; local state-feedback; LMIsReferences:
| [1] | Mahmoud, Large Scale Control Systems: Theories and Techniques (1985) · Zbl 0628.93001 |
| [2] | Siljak, Decentralized Control of Complex Systems (1991) |
| [3] | Hu, Decentralized stabilization of large-scale interconnected systems with delays, IEEE Trans. Autom. Control 39 (1) pp 180– (1994) · Zbl 0796.93007 · doi:10.1109/9.273363 |
| [4] | Iftar, Decentralized control strategies for dynamic routing, Optim. Control Appl. Methods 23 pp 329– (2002) · Zbl 1072.93500 · doi:10.1002/oca.717 |
| [5] | Kobayashi, Stability of large space structures preserved under failures and local controllers, IEEE Trans. Autom. Control 52 (2) pp 318– (2007) · Zbl 1366.74060 · doi:10.1109/TAC.2006.887897 |
| [6] | Langbort, Decentralized stabilization of linear continuous or discrete-time systems with delays in the interconnection, IEEE Trans. Autom. Control 49 (9) pp 1502– (2004) · Zbl 1365.93141 · doi:10.1109/TAC.2004.834123 |
| [7] | Lee, Decentralized stabilization of a new class of linear discrete large-scale systems with delay, IEEE Trans. Autom. Control 32 (5) pp 757– (1987) |
| [8] | Lozano, Dissipative Systems Analysis and Control: Theory and Applications (2000) · doi:10.1007/978-1-4471-3668-2 |
| [9] | Mahmoud, Robust and stabilization of interconnected systems with delays, IEE Proc. Control Theory Appl. 145 pp 558– (1998) · doi:10.1049/ip-cta:19982406 |
| [10] | Mahmoud, Stability and positive realness for time-delay systems, Int. J. of Math. Anal. Appl. 239 pp 7– (1999) · Zbl 0939.93034 · doi:10.1006/jmaa.1999.6455 |
| [11] | Mahmoud, Passivity and passification of time-delay systems, J. Math. Anal. Appl. 292 pp 247– (2004) · Zbl 1084.93014 · doi:10.1016/j.jmaa.2003.11.055 |
| [12] | Mahmoud, Decentralized stabilization of interconnected systems with time-varying delays, IEEE Trans. Autom. Control 54 (11) pp 2663– (2009) · Zbl 1367.93524 · doi:10.1109/TAC.2009.2031572 |
| [13] | Mahmoud, Decentra-lized stabilization of interconnected systems with time-varying delays, European J. Control 15 (6) pp 624– (2009) · Zbl 1187.93002 · doi:10.3166/ejc.15.624-633 |
| [14] | Mahmoud, Decentralized Control and Filtering in Interconnected Dynamical Systems (2010) · Zbl 1226.93004 · doi:10.1201/b10349 |
| [15] | Oucheriah, Decentralized stabilization of large-scale systems with multiple delays in the interconnection, Int. J. Control 73 pp 1213– (2000) · Zbl 1042.93004 · doi:10.1080/002071700417858 |
| [16] | Pagilla, A decentralized output feedback controller for a class of large-scale interconnected nonlinear systems, J. Dyn. Syst., Meas. Control 127 pp 167– (2005) · doi:10.1115/1.1870047 |
| [17] | Siljak, Robust decentralized turbine/governor using linear matrix inequalities, IEEE Trans. Power Syst. 17 pp 715– (2002) · doi:10.1109/TPWRS.2002.800959 |
| [18] | Tong, Robust stabilization of nonlinear time-delay interconnected systems via decentralized fuzzy control, Int. J. Innov. Comp. Inf. Control 4 (7) pp 1567– (2008) |
| [19] | Wang , Y. C. de-Souze L. H. Xie Decentra-lized output feedback control of interconnected uncertain delay systems 38 42 1993 |
| [20] | Boyd, Linear Matrix Inequalities in System and Control Theory (1994) · Zbl 0816.93004 · doi:10.1137/1.9781611970777 |
| [21] | Chen , J. L. L. Lee Passivity approach to feedback connection stability for discrete-time descriptor systems 2865 2866 |
| [22] | Xu, Positive real control for uncertain singular time-delay systems via output feedback controllers, European J. Control 292 pp 122– (2004) · Zbl 1293.93361 |
| [23] | Hill, Dissipative dynamical systems: basic input-output and state properties, J. Franklin Inst. 309 pp 327– (1980) · Zbl 0451.93007 · doi:10.1016/0016-0032(80)90026-5 |
| [24] | Fridman, On-delay-dependent passivity, IEEE Trans. Autom. Control 47 pp 664– (2002) · Zbl 1364.93370 · doi:10.1109/9.995046 |
| [25] | Benzaouia, Stabilization of positive switching linear discrete-time systems, Int. J. Innov. Comp. Inf. Control 6 (6) pp 2427– (2010) |
| [26] | Boukas, Stabilization of linear systems via delayed state feedback controller, ICIC Exp. Lett. 2 (1) pp 1– (2008) |
| [27] | Wu, Delay-dependent robust stabilization of uncertain singular systems with state delay, ICIC Exp. Lett. 1 (2) pp 169– (2007) · Zbl 1164.93407 · doi:10.1049/el:20073694 |
| [28] | Zhao, Stability and stabilization of delayed T-S fuzzy systems: a delay partitioning approach, IEEE Trans. Fuzzy Syst. 17 (4) pp 750– (2009) · doi:10.1109/TFUZZ.2008.928598 |
| [29] | Zhao, A new approach to guaranteed cost control of T-S fuzzy dynamic systems with interval parameter uncertainties, IEEE Trans. Syst. Man Cybern. 39 (6) pp 1516– (2009) · doi:10.1109/TSMCB.2009.2020295 |
| [30] | Chen, Robust decentra-lized control for interconnected descriptor systems with norm-bounded uncertainties, Asian J. Control 11 (1) pp 78– (2009) · doi:10.1002/asjc.83 |
| [31] | Chen, Globally decentralized adaptive backstepping neural network tracking control for unknown nonlinear interconnected systems, Asian J. Control 12 (1) pp 96– (2010) |
| [32] | Yang, Stochastic switched controller design of networked control systems with a random long delay, Asian J. Control 13 (2) pp 255– (2011) · Zbl 1222.93026 · doi:10.1002/asjc.280 |
| [33] | Ye, Reliable guaranteed cost control for linear state delayed systems with adaptive memory state feedback controllers, Asian J. Control 10 (6) pp 678– (2008) · doi:10.1002/asjc.68 |
| [34] | Zhao, Delay-dependent stability criterion and analysis for Markovian jump systems with time-varying delays, Asian J. Control 13 (2) pp 232– (2011) · Zbl 1222.93234 · doi:10.1002/asjc.302 |
| [35] | Anderson, Modern Analysis and Synthesis: A Modern Systems Theory Approach (1973) |
| [36] | Xie, Robust dissipative control for linear systems with dissipative uncertainty, Int. J. Control 70 pp 169– (1998) · Zbl 0930.93068 · doi:10.1080/002071798222352 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
