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Global almost disturbance decoupling with stability for non minimum-phase single-input single-output nonlinear systems. (English) Zbl 0877.93055

Summary: The so-called problem of almost disturbance decoupling with internal stability (ADDPS) is the following one. Given a system and an (arbitrarily small) number \(\gamma >0\), find a feedback law yielding a closed loop system which is stable and in which the gain (in the \(L_{2}\) sense) between the exogenous input and the regulated output is less than or equal to \(\gamma\) . The complete solution of this problem has been known since a long time in the case of linear systems. In the case of nonlinear systems, the only global results available so far in the literature were about SISO systems having an asymptotically stable zero dynamics. In this paper, a new set of results are presented, dealing with nonlinear SISO systems having a possibly unstable zero dynamics, which include the (general) class of linear SISO systems as a special case.

MSC:

93B52 Feedback control
93C10 Nonlinear systems in control theory
93C73 Perturbations in control/observation systems
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References:

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