| UGAS and ULES of Nonautonomous Systems: Applications to Integral Control of Ships and Manipulators (1998) | |||||||||||||||
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| Nonlinear, adaptive backstepping design is applied to the tracking control problem for a class of mechanical systems with constant disturbances. The adaptive algorithm provides integral action that guarantees zero steady-state tracking error. The main contribution of this paper is to show that the (time-varying) closed-loop tracking error system has an equilibrium, corresponding to zero steadystate tracking error, that is uniformly globally asymptotically stable (UGAS) and uniformly locally exponentially stable (ULES). These properties (and a uniform local Lipschitz condition) guarantee robustness of stability while weaker properties, like uniform global stability plus global convergence, do not. Notation: k\Deltak stands for the Euclidean norm of vectors and induced norm of matrices. k\Deltak 1 denotes the L1 norm. We denote by B r the set B r 4 = fx 2 IR n : kxk rg. A continuous function ff : IR 0 ! IR 0 is said to be of class K, ff 2 K, if ff(s) is strictly increasing and ff... | |||||||||||||||
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