Abstract
with scalar control, where A(x) = (a1(x), . . . , an(x)) , B(x) = (b1(x), . . . , bn(x)) , ai(x), bi(x) belong to C∞(Ω), i = 1, . . . , n, and Ω is an open set containing the equilibrium x = 0, we solve the problem of global stabilization of the zero equilibrium and construct a Lyapunov function for the closed system. An arbitrary smooth function of the state of system (1) is referred to as a virtual output. The solution of the stabilization problem via static or dynamic state feedback is based on finding virtual outputs for which system (1) is minimum phase [1, p. 42; 2]. Existence conditions for such virtual outputs in the cases to be studied were obtained in [2], where the corresponding problems of local stabilization of the zero equilibrium via static state feedback were also solved.
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