# zbMATH — the first resource for mathematics

Iterative algorithm for improved measures of stability robustness for linear state-space models. (English) Zbl 0683.93029
Summary: The problem of robust stability of linear time-invariant systems in state-space models is considered. An iterative algorithm based on the frequency domain approach is proposed which leads to new stability robustness measures. The case of structural perturbations is considered and the new bounds are shown to be a significant improvement over recent ones reported [cf. L. Qiu and E. J. Davison, Proc. 25th IEEE Conf. Decis. Control, Athens/Greece 1986, Vol. 2, 751-755 (New York 1986)]. In addition, it is shown that the directional information on structured perturbations can easily be incorporated in the new robustness criterion. Several illustrative examples are worked out.
##### MSC:
 93B35 Sensitivity (robustness) 93B40 Computational methods in systems theory (MSC2010) 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93C05 Linear systems in control theory
Full Text:
##### References:
 [1] JUANG , Y. T. , Kuo , T. S. , and Hsu , S. F. , 1986 , Stability robustness analysis for state space models .Proc. 25th Conf. on Decision and Control, Athens . [2] DOI: 10.1016/0005-1098(76)90076-5 · Zbl 0323.93020 [3] DOI: 10.1080/0020718508961205 · Zbl 0577.93052 [4] LENTOMAKI N. A., Practical robustness measures in multivariable control, Ph.D. Dissertation (1981) [5] PATEL , R. V. , and TODA , M. , 1980 , Quantitative measures of robustness for multivariable systems .Proc. Joint Automatic Control Conference, paper TD8-A . [6] DOI: 10.1016/0098-1354(78)80016-7 [7] PETKOVSKI , D. B. , and ATHANS , M. , 1981 , Robustness of decentralized output control design with application to electric power systems .Proc. 3rd IMA Conf. on Control Theory, Sheffield , Academic Press , 859 . · Zbl 0507.93008 [8] DOI: 10.1080/00207177908922800 · Zbl 0498.93018 [9] DOI: 10.1109/TAC.1981.1102556 · Zbl 0462.93019 [10] Proc. Instn elect. Engrs,Pt D, 129 , No. 6 (Special Issue on Sensitivity and Robustness in Control Systems Theory and Design) . [11] QIU , L. , and DAVISON , E. J. , 1986 , New perturbation bounds for the robust stability of linear state space models .Proc. 25th Conf. on Decision and Control, Athens . [12] DOI: 10.1109/TAC.1977.1101470 · Zbl 0356.93016 [13] DOI: 10.1109/TAC.1985.1103996 · Zbl 0557.93059
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.