zbMATH — the first resource for mathematics

A new method for variable structure control system design: A linear matrix inequality approach. (English) Zbl 0911.93022
A design method of sliding surfaces for linear control systems (in the presence of uncertainties) is proposed. The sliding surfaces are linear with respect to the state. They are characterized in terms of linear matrix inequalities. So, one can design sliding-mode controllers for even large-scale uncertain systems by solving numerically these inequalities. Moreover, a sufficient condition for the stability of a variable structure control system with mismatched uncertainties is established. An illustrative example is also presented.

93B12 Variable structure systems
15A39 Linear inequalities of matrices
93A15 Large-scale systems
Full Text: DOI
[1] Boyd, S.; Ghaoni, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia
[2] Chen, Y.H., Modified adaptive robust control system design, Int. J. control, 49, 1869-1882, (1989) · Zbl 0683.93027
[3] Choi, H.H.; Chung, M.J., Estimation of the asymptotic stability region of uncertain systems with bounded sliding mode controllers, IEEE trans. automat. control, AC-39, 2275-2278, (1994) · Zbl 0825.93643
[4] Corless, M.J.; Leitmann, G., Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE trans. automat. control, AC-26, 1139-1144, (1981) · Zbl 0473.93056
[5] DeCarlo, R.A.; Zak, S.H.; Mathews, G.P., Variable structure control of nonlinear multivariable systems: a tutorial, (), 212-232
[6] El-Ghezawi, O.M.E.; Zinober, A.S.I.; Billings, S.A., Analysis and design of variable structure systems using a geometric approach, Int. J. control, 38, 657-671, (1983) · Zbl 0538.93035
[7] Packard, A.; Zhou, K.; Pandey, P.; Becker, G., A collection of robust control problems leading to lmis, (), 1245-1250
[8] Utkin, V.I., Variable structure systems with sliding modes, IEEE trans. automat. control, AC-22, 212-222, (1977) · Zbl 0382.93036
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.