# zbMATH — the first resource for mathematics

Robust control of a class of nonlinear systems. (English) Zbl 0910.93069
A nominal nonlinear, continuous-time, multi-input state system $$\dot x = f(x,t) + B(x,t) u$$ is considered. The author derives a sufficient condition so that a set of uncertain systems ($$f$$ and $$B$$ are disturbed additively) is locally uniformly bounded. It is not assumed that the nominal uncontrolled system is stable.
##### MSC:
 93D21 Adaptive or robust stabilization 93C10 Nonlinear systems in control theory 93C73 Perturbations in control/observation systems
##### Keywords:
robust stabilization
Full Text:
##### References:
 [1] B. Brogliato, A. T. Netto: Practical stabilization of a class of nonlinear systems with partially known uncertainties. Automatica 31 (1995), 1, 145-150. · Zbl 0825.93650 [2] M. Corless: Control of uncertain nonlinear systems. ASME J. Dynam. Syst. Meas. Control 115 (1993), 362-372. · Zbl 0775.93088 [3] M. Corless, G. Leitman: Adaptive control of systems containing uncertain functions and unknown functions with uncertain bounds. J. Optim. Theory Appl. 41 (1983), 155-168. · Zbl 0497.93028 [4] A. F. Filipov: Differential equations with discontinuous right-hand size. Differentsialnye Uravneniya XV (1979), 10, 1814-1823. In Russian. [5] A. L. Fradkov: Adaptive Control of Complex Systems. Nauka, Moscow 1990. In Russian. · Zbl 0732.93046 [6] R. A. Freeman, P. V. Kokotovic: Backstepping design of robust controllers for a class of nonlinear systems. NOLCOS, Bordeaux 1992, pp. 307-312. [7] S. Gutman: Uncertain dynamical systems. A Lyapunov min-max approach. IEEE Trans. Automat. Control AC-24 (1979), 437-443. · Zbl 0416.93076 [8] G. Leitman: On one approach to the control of uncertain systems. ASME J. Dynam. Syst. Meas. Control 115 (1993), 372-382. [9] G. Leitman: One method for robust control of uncertain systems: Theory and practice. Kybernetika 32 (1996), 1, 43-62. [10] Feng Lin R. D. Brand, Jing Sun: Robust control of nonlinear systems: Compensating for uncertainty. Internat. J. Control 56 (1995), 6, 1453-1459. · Zbl 0771.93018 [11] Zhihua Qu: Asymptotic stabiłity of controlling uncertain dynamical systems. Internat. J. Control 59 (1994), 5, 1345-1355. · Zbl 0806.93044 [12] Zhihua Qu, J. Dorsey: Robust control by two Lyapunov functions. Internat. J. Control 55 (1992), 6, 1335-1350. · Zbl 0751.93019 [13] Zhihua Qu, J. Dorsey: Robust control of generalized dynamic systems without the matching conditions. ASME J. Dynam. Syst. Meas. Control 113 (1991), 582-589. · Zbl 0745.93063 [14] C. E. Rohrs L. Valavani M. Athans, G. Stein: Robustness of continuous-time adaptive control algorithms in the presence of unmodelled dynamics. IEEE Trans. Automat. Control AC-30 (1985), 9, 881-889. · Zbl 0571.93042 [15] V. Veselý: Large scale dynamic system stabilization using the principle of dominant subsystem approach. Kybernetika 29 (1993), 1, 48-61. · Zbl 0790.93122
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.