Decentralized dynamic output feedback for robust stabilization of a class of nonlinear interconnected systems. (English) Zbl 1117.93057

Summary: The objective of this paper is to propose an approach to robust stabilization of systems which are composed of linear subsystems coupled by nonlinear time-varying interconnections satisfying quadratic constraints. The proposed algorithms, which are formulated within the convex optimization framework, employ linear dynamic feedback structure involving local Luenberger-type observers. It is also shown how the new methodology can produce improved results if interconnections have linear parts that are known a priori. Examples of output stabilization of inverted pendulums and decentralized control of a platoon of vehicles are used to illustrate the applicability of the design method.


93D15 Stabilization of systems by feedback
93C10 Nonlinear systems in control theory
90C25 Convex programming
93B05 Controllability


LMI toolbox
Full Text: DOI


[1] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia · Zbl 0816.93004
[2] Cao, Y.Y.; Sun, Y.X.; Mao, W.J., Output feedback decentralized stabilization: ILMI approach, Systems & control letters, 35, 183-194, (1998) · Zbl 0909.93060
[3] Chu, D.; Šiljak, D.D., A canonical form for the inclusion principle of dynamic systems, SIAM journal on control and optimization, 44, 969-990, (2005) · Zbl 1130.93312
[4] Dullerud, G.E.; Paganini, F., A course in robust control theory— a convex approach, (2000), Springer New York · Zbl 0939.93001
[5] Gahinet, P.; Apkarian, P., A linear matrix inequality approach to \(H_\infty\) control, International journal of robust and nonlinear control, 4, 421-448, (1994) · Zbl 0808.93024
[6] Gahinet, P., Nemirovski, A., Laub, A.J., & Chilali, M. (1995). LMI control toolbox, Natick, MA: The Math Works.
[7] Garcia, G.; Daafouz, J.; Bernussou, J., The infinite time near optimal decentralized regulator problem for singularly perturbed systems: a convex optimization approach, Automatica, 38, 1397-1406, (2002) · Zbl 1008.93054
[8] Geromel, J.C.; Bernussou, J.; de Oliveira, M.C., \(H_2\)-norm optimization with constrained dynamic output feedback controllers: decentralized and reliable control, IEEE transactions on automatic control, 44, 1449-1454, (1999) · Zbl 0954.93003
[9] Geromel, J.C.; Bernussou, J.; Peres, P.L.D., Decentralized control through parameter space optimization, Automatica, 30, 1565-1578, (1994) · Zbl 0816.93036
[10] Ho, D.W.C.; Lu, G., Robust stabilization for a class of discrete-time non-linear systems via output feedback: the unified LMI approach, International journal of control, 76, 105-115, (2003) · Zbl 1026.93048
[11] Iwasaki, T.; Skelton, R.E., All controllers for the general \(H_\infty\) control problem: LMI existence conditions and state space formulas, Automatica, 30, 1307-1317, (1994) · Zbl 0806.93017
[12] Kwakernaak, H.; Sivan, R., Linear optimal control systems, (1972), Wiley New York · Zbl 0276.93001
[13] Li, K.; Kosmatopoulos, E.B.; Yoannou, P.A.; Ryciotaki-Boussalis, H., Large segmented telescopes: centralized decentralized and overlapping control designs, IEEE control systems magazine, 20, 59-72, (2000)
[14] Pagilla, P.R.; Zhu, Y., A decentralized output feedback controller for a class of large-scale interconnected nonlinear systems, Journal of dynamic systems measurement and control—transactions of the ASME, 127, 167-172, (2005)
[15] Qi, X.; Salapaka, M.V.; Voulgaris, P.G.; Khammash, M., Structured optimal and robust control with multiple criteria: A convex solution, IEEE transactions on automatic control, 49, 1623-1640, (2004) · Zbl 1365.93270
[16] Scorletti, G.; Duc, G., An LMI approach to decentralized control, International journal of control, 74, 211-224, (2001) · Zbl 1033.93020
[17] Šiljak, D.D., Decentralized control of complex systems, (1991), Academic Press New York · Zbl 0382.93003
[18] Šiljak, D.D.; Stipanović, D., Robust stabilization of nonlinear systems, Mathematical problems in engineering, 6, 461-493, (2000) · Zbl 0968.93075
[19] Šiljak, D.D.; Stipanović, D., Autonomous decentralized control, Proceedings of ASME international mechanical engineering congress, 761-765, (2001)
[20] Šiljak, D.D.; Zečević, A.I., Control of large-scale systems: beyond decentralized feedback, Annual revision in control, 20, 169-179, (2004) · Zbl 1365.93028
[21] Stanković, S.S., & Šiljak, D.D., (2006). Robust stabilization of nonlinear interconnected systems by decentralized dynamic output feedback. IEEE Transactions on Automatic Control, submitted.
[22] Stanković, S.S.; Stanojević, M.J.; Šiljak, D.D., Decentralized overlapping control of a platoon of vehicles, IEEE transactions on control systems technology, 8, 816-832, (2000)
[23] Yang, G.H.; Wang, J.L., Decentralized controller design for composite systems: linear case, International journal of control, 72, 815-825, (1999) · Zbl 0945.93014
[24] Zečević, A.I.; Nešković, G.; Šiljak, D.D., Robust decentralized exciter control with linear feedback, IEEE transactions on power systems, 19, 1096-1103, (2004)
[25] Zečević, A.I.; Šiljak, D.D., Design of robust static output feedback for large-scale systems, IEEE transactions on automatic control, 49, 2040-2044, (2004) · Zbl 1365.93028
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.