The Construction of Minimal Phase Affine Systems

Abstract

A(x) = (a1(x), . . . , an(x)) T , B(x) = (b1(x), . . . , bn(x)) T , ai(x), bi(x) ∈ C∞(Ω), and Ω is an open set containing the equlibrium point x = 0, equipped with the output y = h(x), h(x) ∈ C∞(Ω), h(0) = 0, (2) the stabilization problem for the state x = 0 can be solved by the stabilization of the zero output value provided that system (1), (2) is minimal phase. This is especially important if the information on the state of system (1) can be obtained only with the use of the output (2). However, even in the case of complete measurement of the state of system (1), the use of minimal phase systems often permits one to widen the set of stabilizing feedbacks substantially (see examples in Section 2). To use this approach for the solution of the stabilization problem for the equilibrium state x = 0 of system (1), one should find an output (2) such that system (1), (2) is minimal phase. Conditions guaranteeing the existence of such outputs for system (1) and related search methods are presented in Sections 3 and 4. In Section 1, we give definitions and results pertaining to stabilization of minimal phase systems [1, pp. 137–174].