Stability and guaranteed cost control of uncertain discrete delay systems. (English) Zbl 1083.93045

Fridman, E.; Shaked, U.

Int. J. Control 78, No. 4, 235-246 (2005).

Linear discrete-time systems with uncertain delay and norm-bounded parameter perturbations are considered. First, linear matrix inequality conditions for asymptotic stability are derived for the delay-dependent and delay-independent cases. Then these results are extended to the guaranteed quadratic cost control by constant state feedback. Examples are provided to illustrate the application of the theory developed.

Reviewer: Edwin Engin Yaz (Milwaukee)

MSC:

93D09	Robust stability
93D21	Adaptive or robust stabilization
93C55	Discrete-time control/observation systems
93C05	Linear systems in control theory
15A39	Linear inequalities of matrices

Keywords:

robust stability; adaptive or robust stabilization; discrete-time systems; linear systems; uncertain delay; linear matrix inequality; guaranteed quadratic cost control

References:

[1]	DOI: 10.1049/ip-cta:20030572 · doi:10.1049/ip-cta:20030572
[2]	DOI: 10.1016/S0167-6911(01)00114-1 · Zbl 0974.93028 · doi:10.1016/S0167-6911(01)00114-1
[3]	Fridman E, Proceedings of MTNS (2004)
[4]	DOI: 10.1109/TAC.2002.804462 · Zbl 1364.93564 · doi:10.1109/TAC.2002.804462
[5]	DOI: 10.3166/ejc.11.29-37 · Zbl 1293.93672 · doi:10.3166/ejc.11.29-37
[6]	DOI: 10.1080/00207170410001663525 · Zbl 1066.93009 · doi:10.1080/00207170410001663525
[7]	DOI: 10.1016/S0005-1098(98)00054-5 · Zbl 0934.93023 · doi:10.1016/S0005-1098(98)00054-5
[8]	DOI: 10.1016/S0005-1098(02)00195-4 · Zbl 1014.93031 · doi:10.1016/S0005-1098(02)00195-4
[9]	DOI: 10.1109/9.763213 · Zbl 0964.34065 · doi:10.1109/9.763213
[10]	Lee YS, Proceedings of the 15th IFAC Congress on Automation and Control (2002)
[11]	DOI: 10.1016/S0005-1098(97)00082-4 · doi:10.1016/S0005-1098(97)00082-4
[12]	DOI: 10.1016/S0005-1098(99)00158-2 · Zbl 0982.93032 · doi:10.1016/S0005-1098(99)00158-2
[13]	DOI: 10.1080/00207170110067116 · Zbl 1023.93055 · doi:10.1080/00207170110067116
[14]	Niculescu S-I, Delay Effects on Stability: A Robust Control Approach (2001)
[15]	DOI: 10.1016/S0005-1098(99)00057-6 · Zbl 0936.93019 · doi:10.1016/S0005-1098(99)00057-6
[16]	DOI: 10.1016/0167-6911(94)00041-S · Zbl 0883.93035 · doi:10.1016/0167-6911(94)00041-S
[17]	Verriest E, Proceedings of the IEEE Conference on Decision and Control pp pp. 386–391– (1995)
[18]	DOI: 10.1109/9.286258 · Zbl 0807.93055 · doi:10.1109/9.286258
[19]	DOI: 10.1080/00207179608921866 · Zbl 0841.93014 · doi:10.1080/00207179608921866
[20]	DOI: 10.1016/j.sysconle.2003.08.002 · Zbl 1157.93371 · doi:10.1016/j.sysconle.2003.08.002
[21]	DOI: 10.1016/S0005-1098(99)00061-8 · Zbl 0959.93048 · doi:10.1016/S0005-1098(99)00061-8
[22]	DOI: 10.1016/S0898-1221(98)80041-2 · Zbl 0933.39011 · doi:10.1016/S0898-1221(98)80041-2