zbMATH — the first resource for mathematics

Delay-dependent robust \(H_\infty \) control for uncertain discrete-time singular systems with time-delays. (English) Zbl 1142.93011
Summary: The robust memoryless state feedback \(H_{\infty }\) control problem for uncertain time-delay discrete-time singular systems is discussed. Under a series of equivalent transformation, the equivalence of this problem and the robust state feedback \(H_{\infty }\) control problem for standard state-space uncertain time-delay discrete-time systems is presented. In terms of matrix inequality, the delay-dependent sufficient condition for the solution of this problem is given, the design method of the memoryless state feedback controller and the controller are also given.

93B36 \(H^\infty\)-control
93C55 Discrete-time control/observation systems
93C41 Control/observation systems with incomplete information
Full Text: DOI
[1] Aplevich, J.D., Implicit linear systems, (1991), Springer Berlin · Zbl 0764.93001
[2] Boukas, E.K.; Al-Muthairi, N.F., Delay-dependent stabilization of singular linear systems with delays, Internat. J. innovative comput. inform. and control, 2, 2, 283-291, (2006)
[3] Campbell, S.L., Singular system of differential equations, vol. II, (1982), Pitman San Francisco · Zbl 0482.34008
[4] Chen, B.; Lam, J.; Xu, S., Memory state feedback guaranteed cost control for neutral delay systems, Internat. J. innovative comput. inform. and control, 2, 2, 293-303, (2006)
[5] Dai, L., Singular control systems, ()
[6] EI Ghaoui, L.; Oustry, F.; AitRami, M., A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE trans. automat. control, 42, 8, 1171-1176, (1997) · Zbl 0887.93017
[7] Feng, J.; Zhu, S.; Cheng, Z., Guaranteed cost control of linear uncertain singular time-delay systems, (), 1802-1807
[8] Fridman, E.; Shaked, U., A descriptor system approach to \(H_\infty\) control of linear time-delay systems, IEEE trans. automat. control, 47, 2, 253-270, (2002) · Zbl 1364.93209
[9] Fridman, E.; Shaked, U., Delay-dependent stability and \(H_\infty\) control: constant and time-varying delays, Internat. J. control, 76, 1, 48-60, (2003) · Zbl 1023.93032
[10] Kapila, V.; Haddad, W.M., Memoryless \(H_\infty\) controllers for discrete-time systems wity time delay, Automatica, 34, 1141-1144, (1998) · Zbl 0934.93023
[11] Lee, Y.S.; Moon, Y.S.; Kwon, W.H.; Park, P.G., Delay-dependent robust \(H_\infty\) control for uncertain systems with a state-delay, Automatica, 40, 1, 65-72, (2004) · Zbl 1046.93015
[12] S.P. Ma, Z.L. Cheng, An lmi approach to robust stabilization for uncertain discrete-time singular systems, in: Proceedings of the 41st IEEE CDC, Las Vegas, Nevada, USA, 2002, pp. 1090-1095.
[13] Mahmoud, M.S., Robust \(H_\infty\) control of discrete systems with uncertain parameters and unknown delays, Automatica, 36, 627-635, (2000) · Zbl 0982.93032
[14] Moon, Y.S.; Park, P.G.; Kwon, W.H.; Lee, Y.S., Delay-dependent robust stabilization of uncertain state-delayed systems, Internat. J. control, 74, 14, 1447-1455, (2001) · Zbl 1023.93055
[15] Palhares, R.M.; Campos, C.D.; Leles, M.C.R.V.; Ekel, P.Ya.; D’Angelo, M.F.S., On delay-dependent robust \(H_\infty\) control of uncertain continuous- and discrete-time linear systems with lumped delays, (), 4032-4036
[16] Shi, P.; Boukas, E.K., On \(H_\infty\) control design for singular continuous-time delay systems with parametric uncertainties, Nonlinear dynamics and systems theory, 4, 1, 59-71, (2004) · Zbl 1073.93020
[17] Shi, P.; Boukas, E.-K.; Shi, Y.; Agarwal, R.K., Optimal guaranteed cost control of uncertain discrete time-delay systems, J. comput. appl. math., 157, 435-451, (2003) · Zbl 1029.93044
[18] Song, S.H.; Kim, J.K., \(H_\infty\) control of discrete-time linear systems with norm-bounded uncertainties and time delay in state, Automatica, 34, 137-139, (1998) · Zbl 0904.93011
[19] Xie, L., Output feedback \(H_\infty\) control of systems with parameter uncertainty, Internat. J. control, 63, 741-750, (1996) · Zbl 0841.93014
[20] Xu, S.; Lam, J.; Yang, C., Robust \(H_\infty\) control for discrete singular systems with state delay and parameter uncertainty, Dynamics continuous discrete impul. systems, 11, 3, 497-506, (2002)
[21] Xu, S.; Lam, J.; Yang, C., Robust \(H_\infty\) control for uncertain singular systems with state-delay, Internat. J. robust and nonlinear control, 13, 3, 1213-1223, (2003) · Zbl 1039.93019
[22] Yuan, L.; Achenie, L.E.K.; Jiang, W., Robust \(H_\infty\) control for linear discrete-time systems with norm-bounded time delay uncertainty, Systems control lett., 27, 199-208, (1996) · Zbl 0875.93108
[23] Yue, D.; Lam, J.; Ho, D.W.C., Reliable \(H_\infty\) control of uncertain descriptor systems with multiple delays, IEE proc. control theory and appl., 150, 6, 557-564, (2003)
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.