The robust stability of linear systems with unstructured, structured or non-linear perturbations is investigated in a unifying framework. New sufficient conditions in terms of matrix Riccati inequalities are obtained. Some previously known results are generalized.
KharitonovV. L.Asymptotic stability of a family of systems of linear differential equations. Differentsial'nye Uravneniya, 1978, 14 (11), 2086–2088.
2.
ŜiljakD. D.Parameter space methods for robust control design: A guided tour. IEEE Trans. Autom. Control, 1989, 34 (7), 674–688.
3.
MansourM.Robust stability of interval matrices. In Proceedings of 28th IEEE Conference on Decision and Control, December 1989, pp. 46–51.
4.
JuryE.Robustness of a discrete system. Automn Remote Control, 1990, 51 (5), 571–589.
5.
MansourM.BalemiS.TruölW. (Ed.) Robustness of Dynamic Systems with Parameter Uncertainties, 1992 (Birkhäuser, Boston).
6.
DorateP.YedavalliR. K. (Eds) Recent Advances in Robust Control, 1990 (IEEE Press, Piscataway, New Jersey).
7.
HinrichsenD.PritchardA. J.Robustness measures for linear systems with application to stability radii of Hurwitz and Schur polynomials. Int. J. Control, 1992, 55 (4), 809–844.
8.
FangY.LoparoK. A.FengX.A sufficient condition for stability of a polytope of interval matrices. Systems Control Lett., 1994, 23 (4), 237–245.
9.
FangY.LoparoK. A.FengX.Sufficient conditions for the stability of interval matrices. Int. J. Control, 1993, 58, 969–977.
10.
FangY.LoparoK. A.FengX.Robust stability analysis of uncertain systems via matrix measure (submitted for publication).
11.
PatelR. V.TodaM.Quantitative measures of robustness for multivariable systems. In Proceedings of Joint Conference on Automatic Control, San Francisco, California, 1980, paper TD8-A.
12.
YedavalliR. K.Improved measures of stability robustness for linear state space models. IEEE Trans. Autom. Control, 1985, 30 (6), 577–579.
13.
ZhouK.KhargonekarP. P.Stability robustness bounds for linear state space models with structured uncertainty. IEEE Trans. Autom. Control, 1987, 32 (7), 621–623.
14.
YedavalliR. K.LiangZ.Reduced conservatism in stability robustness bounds by state transformation. IEEE Trans. Autom. Control, 1986, 31, 863–866.
15.
YedavalliR. K.On measures of stability robustness for linear state space systems with real parameter perturbations: A perspective. 1989 ACC Proc., June 1989.
16.
FangY.LoparoK. A.Stability robustness bounds and robust stability for linear systems with structured uncertainty. In Proceedings of American Control Conference, Baltimore, Maryland, 1994, pp. 221–225.
17.
DoyleJ. C.GloverK.KhargonekarP. P.FrancisB. A.State space solutions to standard H2 and H∞ control problems. IEEE Trans. Autom. Control, 1989, 37831–847.
18.
HinrichsenD.PritchardA. J.Stability radii of linear systems. Systems Control Lett., 1986, 7, 1–10.
19.
PandolfiL.ZwartH.Stability of perturbed linear distributed parameter systems. Systems Control Lett., 1991, 17, 257–264.
20.
WangY.XieL.de SouzaC. E.Robust control of a class of uncertain non-linear systems. Systems Control Lett., 1992, 519, 139–149.
