×

Delay-dependent robust \(H_{\infty}\) control for uncertain systems with a state-delay. (English) Zbl 1046.93015

Delay-dependent robust \(H_\infty\) control for uncertain systems with a state-delay is proposed. A new delay-dependent bounded real lemma is presented. A Lyapunov-Krasovskij functional which helps to avoid model transformations is constructed. Matrix inequalities including nonlinear terms are applied.

MSC:

93B36 \(H^\infty\)-control
93C23 Control/observation systems governed by functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Choi, H. H.; Chung, M. J., An LMI approach to \(H_∞\) controller design for linear time-delay systems, Automatica, 33, 4, 737-739 (1997) · Zbl 0875.93104
[2] de Souza, C. E.; Li, X., Delay-dependent robust \(H_∞\) control of uncertain linear state-delayed systems, Automatica, 35, 1313-1321 (1999) · Zbl 1041.93515
[3] El Ghaoui, L.; Oustry, F.; Ait Rami, M., A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Transactions on Automatic Control, 42, 8, 1171-1176 (1997) · Zbl 0887.93017
[4] Fridman, E., New Lyapunov-Krasovskii functional for stability of linear retarded and neutral type systems, Systems & Control Letters, 43, 309-319 (2001) · Zbl 0974.93028
[5] Fridman, E.; Shaked, U., New bounded real lemma representations for time-delay systems and their applications, IEEE Transactions on Automatic Control, 46, 1973 (2001) · Zbl 1006.93055
[6] Fridman, E.; Shaked, U., A descriptor system approach to \(H_∞\) control of linear time-delay systems, IEEE Transactions on Automatic Control, 47, 2, 253-270 (2002) · Zbl 1364.93209
[7] Kapila, V.; Haddad, W. M., Memoryless \(H_∞\) controllers for discrete-time systems with time delay, Automatica, 34, 9, 1141-1144 (1998) · Zbl 0934.93023
[8] Kim, J. H.; Park, H. B., \(H_∞\) state feedback control for generalized continuous/discrete time-delay systems, Automatica, 35, 1443-1451 (1999) · Zbl 0954.93011
[9] Lee, Y. S., Moon, Y. S., & Kwon, W. H. (2001). Delay-dependent robust \(H_∞\)Proceedings of conference on decision and control; Lee, Y. S., Moon, Y. S., & Kwon, W. H. (2001). Delay-dependent robust \(H_∞\)Proceedings of conference on decision and control
[10] Moon, Y. S. (1998). Robust control of time-delay systems using linear matrix inequalities; Moon, Y. S. (1998). Robust control of time-delay systems using linear matrix inequalities
[11] Moon, Y. S.; Park, P. G.; Kwon, W. H.; Lee, Y. S., Delay-dependent robust stabilization of uncertain state-delayed systems, International Journal of Control, 74, 14, 1447-1455 (2001) · Zbl 1023.93055
[12] Park, P. (1999). A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Transactions on Automatic Control; Park, P. (1999). A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Transactions on Automatic Control · Zbl 0957.34069
[13] Park, P. G., Moon, Y. S., & Kwon, W. H. (1998). A delay-dependent robust stability criterion for uncertain time-delay systems. In Proceedings of the American control conference; Park, P. G., Moon, Y. S., & Kwon, W. H. (1998). A delay-dependent robust stability criterion for uncertain time-delay systems. In Proceedings of the American control conference
[14] Zribi, M.; Mahmoud, M. S., \(H_∞\)-control design for systems with multiple delays, Computers and Electrical Engineering, 25, 451-475 (1999) · Zbl 0946.93013
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.