Li, Huaizhong; Niculescu, Silviu-Iulian; Dugard, Luc; Dion, Jean-Michel Robust guaranteed cost control of uncertain linear time-delay systems using dynamic output feedback. (English) Zbl 1017.93502 Math. Comput. Simul. 45, No. 3-4, 349-358 (1998). Summary: This paper is concerned with robust guaranteed cost control of uncertain linear time-delay systems using dynamic output feedback. The uncertain systems tackled in this paper involve uncertainty in quadratic constrained form which includes the well-known norm-bounded time-varying uncertainty as a special case. We show that the feasibility of several matrix inequalities guarantees the solvability of the addressed problem. Furthermore, we propose an iterative algorithm to numerically check the feasibility of the concerned matrix inequalities using linear matrix inequalities (LMIs). Cited in 6 Documents MSC: 93B35 Sensitivity (robustness) 93C41 Control/observation systems with incomplete information Keywords:Time-delay systems; Robust control; Guaranteed cost control; Linear matrix inequality PDFBibTeX XMLCite \textit{H. Li} et al., Math. Comput. Simul. 45, No. 3--4, 349--358 (1998; Zbl 1017.93502) Full Text: DOI References: [1] S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15, Philadelphia: SIAM Studies in Appl. Math., 1994 · Zbl 0816.93004 [2] P. Gahinet, Explicit controller formulas for LMI-based H\infty synthesis, Automatica, vol. 32, pp. 1007–1014, 1996 · Zbl 0855.93025 [3] V.B. Kolmanovskii, V.R. Nosov, Stability of Functional Differential Equations, Academic Press, New York, 1986 · Zbl 0593.34070 [4] X. Li, C.E. de Souza, LMI approach to delay-dependent robust stability and stabilization of uncertain linear delay systems, Proc. 34th IEEE CDC., New Orleans, Louisiana, 1995 [5] H. Li, S.I. Niculescu, L. Dugard, J.-M. Dion, Robust Guaranteed Cost Control of Uncertain Linear Time-delay Systems using Dynamic Output Feedback, Internal Report, Laboratoire d’Automatique de Grenoble, 1996 · Zbl 1017.93502 [6] S.I. Niculescu, C.E. de Souza, J.-M. Dion, L. Dugard, Robust stability and stabilization for uncertain linear systems with state delay: Single delay case (I), Proc. IFAC Workshop on Robust Control Design, Rio de Janeiro, Brazil, 1994, pp. 469–474 [7] S.I. Niculescu, A. Trofino-Neto, J.-M. Dion, L. Dugard, Delay-dependent stability of linear systems with delayed state: An LMI approach, Proc. 34th IEEE Conf. Dec. Contr., New Orleans, USA, 1995, pp. 1495–1496 [8] S.I. Niculescu, E.I. Verriest, L. Dugard, J.-M. Dion, Stability and robust stability of time-delay systems: A guided tour, in: L. Dugard, E.I. Verriest (Eds.), Stability and Control of Delay Systems, Springer, LNCIS, 1997 · Zbl 0914.93002 [9] S.O. Reza Moheimani, I.R. Petersen, Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems, Proc. 34th IEEE CDC., New Orleans, USA, 1995, pp. 1513–1518 [10] Shen, J. C.; Chen, B. S.; Kung, F. C.: Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach. IEEE trans. Automat. contr. 36, 638-640 (1991) [11] L. Xie, C.E. de Souza, Robust stabilization and disturbance attenuation for uncertain delay systems, Proc. 2nd European Contr. Conf., Groningen, The Netherlands, 1993, pp. 667–672 [12] V.A. Yakubovich, S-procedure in nonlinear control theory, Vestnik Leningrad University, 1971, pp. 62–77 · Zbl 0232.93010 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.