Abstract
Global stability and instability of a class of LS based discrete-time adaptive nonlinear control systems are investigated in this paper. The systems to be controlled are assumed to be linear in unknown parameters but nonlinear in dynamics which are characterized by a nonlinear function f(x). In the scalar parameter case, it is shown that the certainty equivalence adaptive control is globally stable whenever f(x) has a growth rate |f(x)| = O(||x||b) with 6 < 8 and is not globally stable in general when 6 ≥ 8. Both the results found and the new analytical methods introduced in this paper may be regarded as a basic step for further study.
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