# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
$H_\infty$ control of discrete-time linear systems with norm-bounded uncertainties and time delay in state. (English) Zbl 0904.93011
Summary: This paper deals with an $H_\infty$ control problem for discrete-time linear systems with norm-bounded uncertainties and time delay in the state. In terms of a modified Riccati inequality for discrete-time linear systems, a sufficient condition is presented and a state feedback control law is also given. The proposed control law is a memoryless state feedback control law.

##### MSC:
 93B36 $H^\infty$-control 34K35 Functional-differential equations connected with control problems 93C55 Discrete-time control systems
Full Text:
##### References:
 [1] De Souza, C. E.; Fu, M.; Xie, L.: Analysis and synthesis of discrete-time systems with time-varying uncertainty. IEEE trans. Automat. control 38, 459-462 (1993) · Zbl 0791.93064 [2] Doyle, J. C.; Glover, K.; Khargonekar, P. P.; Francis, B. A.: State-space solutions to standard H2 and H$\infty$control problems. IEEE trans. Automat. control 34, 831-847 (1989) · Zbl 0698.93031 [3] Gu, G.; Mira, P.: Disturbance attenuation and H$\infty$optimization with linear output feedback control. J. guidance control 17, No. 1, 145-152 (1994) · Zbl 0787.93027 [4] Kokame, H.; Konishi, K.; Mori, T.: Robust H$\infty$control for linear delay differential systems with time-varying uncertainties. Proc. 35th conf. Decision and control, 2097-2102 (1996) [5] Jeung, E. T.; Oh, D. C.; Kim, J. H.; Park, H. B.: Robust controller design for uncertain systems with time delays: LMI approach. Automatica 32, No. 8, 1229-1231 (1996) · Zbl 0854.93057 [6] Lee, J. H.; Kim, S. W.; Kwon, W. H.: Memoryless controllers for state delayed systems. IEEE trans. Automatic control 39, 159-162 (1994) · Zbl 0796.93026 [7] Li, H.; Niculescu, S. I.; Dugard, L.; Dion, J. M.: Robust H$\infty$control of uncertain linear time-delay systems: a linear matrix inequality approach. Proc. 35th conf. On decision and control, 1370-1375 (1996) [8] Skelton, R. E.; Stoustup, J.; Limebeer, D. J. N.: The H$\infty$control problem using static output feedback. Int. J. Robust and nonlinear control 4, 449-455 (1994) · Zbl 0806.93019 [9] Stoorvogel, A. A.: The H$\infty$Control problems: A state space approach. (1992) · Zbl 0751.93021 [10] Verriest, E.; Ivanov, A. F.: Robust stability of delay-difference equations. Proc. of the 34th conf. On decision and control, 386-391 (1995) [11] Xie, L.; Fu, M.; De Souza, C. E.: H$\infty$control and quadratic stabilization of systems with parameter uncertainty via output feedback. IEEE trans. Automat. control 37, No. 8, 1253-1256 (1992) · Zbl 0764.93067 [12] Yuan, L.; Achenie, L. E. K.; Jiang, W.: Robust control for linear discrete-time systems with norm-bounded time-varying uncertainty. Syst. control lett. 27, 199-208 (1996) · Zbl 0875.93108 [13] Yuan, L.: Robust H$\infty$analysis and synthesis of linear systems with state-delay and norm-bounded time varying uncertainties. Proc. 35th conf. On decision and control, 2960-2961 (1996)