# 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)
Reliable $H_\infty$ control for discrete-time piecewise linear systems with infinite distributed delays. (English) Zbl 1192.93030
Summary: The reliable $H_\infty$ control problem is investigated for discrete-time piecewise linear systems with time delays and actuator failures. The time delays are assumed to be infinitely distributed in the discrete-time domain, and the possible failure of each actuator is described by a variable varying in a given interval. The aim of the addressed reliable $H_\infty$ control problem is to design a controller such that, for the admissible infinite distributed delays and possible actuator failures, the closed-loop system is exponentially stable with a given disturbance attenuation level $\gamma$. The controller gain is characterized in terms of the solution to a linear matrix inequality that can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.

##### MSC:
 93B36 $H^\infty$-control 93C55 Discrete-time control systems 93C05 Linear control systems 93D20 Asymptotic stability of control systems
Full Text:
##### References:
 [1] Feng, G.: Stability analysis of piecewise discrete-time linear systems, IEEE transactions on automatic control 47, No. 7, 1108-1112 (2002) [2] Gao, H.; Wang, C.; Wang, J.: A delay-dependent approach to robust H$\infty$filtering for uncertain discrete-time state-delayed systems, IEEE transactions on signal processing 52, No. 6, 1631-1640 (2004) [3] Kuang, Y.; Smith, H.; Martin, R.: Global stability for infinite-delay, dispersive Lotka-Volterra systems: weakly interacting populations in nearly identical patches, Journal of dynamics and differential equations 3, No. 3, 339-360 (1991) · Zbl 0731.92029 · doi:10.1007/BF01049736 [4] Liu, Y.; Wang, Z.; Liang, J.; Liu, X.: Synchronization and state estimation for discrete-time complex networks with distributed delays, IEEE transactions on systems, man, and cybernetics - part B 38, No. 5, 1314-1325 (2008) [5] Veillette, R. J.; Medanic, J. V.; Perkins, W. R.: Design of reliable control systems, IEEE transactions on automatic control 37, 293-304 (1992) · Zbl 0745.93025 · doi:10.1109/9.119629 [6] Wang, Z.; Yang, F.; Ho, D. W. C.; Liu, X.: Robust H$\infty$filtering for stochastic time-delay systems with missing measurements, IEEE transactions on signal processing 54, No. 7, 2579-2587 (2006) [7] Xu, J., & Xie, L. (2006). Non-synchronized H\infty estimation of piecewise linear systems. In: Proc. 1st IEEE conference on industrial electronics and applications, Singapore, May 2006 (pp. 1-6) [8] Yang, G. H.; Wang, J. L.; Soh, Y. C.: Reliable H$\infty$controller design for linear systems, Automatica 37, 717-725 (2001) · Zbl 0990.93029