# zbMATH — the first resource for mathematics

Robust control of a class of uncertain nonlinear systems. (English) Zbl 0765.93015
Summary: This paper considers the robust control of a class of nonlinear systems with real time-varying parameter uncertainty. Interest is focused on the design of linear dynamic output feedback control and two problems are addressed. The first one is the robust stabilization and the other is the problem of robust performance in an $$H_ \infty$$ sense. A technique is proposed for designing stabilizing controllers for both problems by converting them into ‘scaled’ $$H_ \infty$$ control problems which do not involve parameter uncertainty.

##### MSC:
 93B35 Sensitivity (robustness) 93C10 Nonlinear systems in control theory
Full Text:
##### References:
 [1] Barmish, B.R., Necessary and sufficient conditions for quadratic stabilizability of an uncertain system, J. optim. theory appl., 46, 399-408, (1985) · Zbl 0549.93045 [2] Barmish, B.R.; Corless, M.; Leitmann, G., A new class of stabilizing controllers for uncertain dynamical systems, SIAM J. control optim., 21, 246-255, (1983) · Zbl 0503.93049 [3] Bergen, A.R., Power system analysis, (1986), Prentice-Hall Englewood Cliffs, NJ [4] Chen, Y.H.; Leitmann, G., Robustness of uncertain systems in the absence of matching assumptions, Internat. J. control, 45, 1527-1542, (1987) · Zbl 0623.93023 [5] Corless, M.; Leitmann, G., Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamical systems, IEEE trans. automat. control, 26, 1139-1144, (1981) · Zbl 0473.93056 [6] Corless, M.; Leitmann, G., Adaptive control of systems containing uncertain functions and unknown functions with uncertain bounds, J. optim. theory appl., 41, 155-168, (1983) · Zbl 0497.93028 [7] Priscoli, F.Delli; Isidori, A., Robust tracking for a class of nonlinear system, () · Zbl 1100.93005 [8] Doyle, J.C.; Glover, K.; Khargonekar, P.P.; Francis, B.A., State-space solutions to the standard $$H\^{}\{2\}$$ and $$H\^{}\{∞\}$$ control problems, IEEE trans. automat. control, 34, 831-847, (1989) · Zbl 0698.93031 [9] Gibbens, P.W.; Fu, M., Output feedback control for output tracking of nonlinear uncertain systems, () [10] Ha, I.J.; Gilbert, E.G., Robust tracking in nonlinear systems, IEEE trans. automat. control, 32, 763-771, (1987) · Zbl 0631.93031 [11] Isidori, A., Nonlinear control systems, (1989), Springer-Verlag New York · Zbl 0714.93021 [12] Khargonekar, P.P.; Petersen, I.R.; Zhou, K., Robust stabilization of uncertain linear systems: quadratic stabilizability and $$H∞$$ control theory, IEEE trans. automat. control, 35, 356-361, (1990) · Zbl 0707.93060 [13] Leitmann, G., Guaranteed asymptotic stability for some systems with bounded uncertainties, Trans. ASME J. dynam. systems measurement and control, 101, 212-216, (1979) · Zbl 0416.93077 [14] Madiwale, A.N.; Haddad, W.M.; Bernstein, D.S., Robust $$H∞$$ control design for systems with structured parameter uncertainty, Systems control lett., 12, 393-407, (1989) · Zbl 0685.93022 [15] Petersen, I.R., Disturbance attenuation and $$H∞$$ optimization: a design method base on the algebraic Riccati equation, IEEE trans. automat. control, 32, 427-429, (1987) · Zbl 0626.93063 [16] Petersen, I.R.; Hollot, C.V., A Riccati equation approach to the stabilization of uncertain linear systems, Automatica, 22, 397-411, (1986) · Zbl 0602.93055 [17] Schmitendorf, W.E., Designing stabilizing controllers for uncertain systems using the Riccati equation approach, IEEE trans. automat. control, 33, 376-379, (1989) · Zbl 0643.93052 [18] Xie, L.; de Souza, C.E., Robust $$H∞$$ control for linear time-invariant systems with norm-bounded uncertainty in the input matrix, Systems control lett., 14, 389-396, (1990) · Zbl 0698.93054 [19] Xie, L.; de Souza, C.E., Robust $$H∞$$ control for a class of uncertain time-invariant systems, (), 479-483 · Zbl 0754.93046 [20] Xie, L.; Fu, M.; de Souza, C.E., $$H∞$$ control and quadratic stabilization of systems with parameter uncertainty via output feedback, IEEE trans. automat. control, 37, (1992), to appear [21] Vidyassagar, M., New directions of research on nonlinear system theory, (), 1060-1091
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.