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Output feedback global stabilization for a class of nonlinear systems with unmodelled dynamics. (English) Zbl 0862.93050
The authors consider a single-input, single-output minimum phase linear plant $\dot x=Fx+gu+\mu h_1g+h_2,\quad y=cx.\tag{1}$ The relative degree may be greater than 1. The system is connected with two nonlinear systems $\dot\xi=q_1(\xi,u),\quad h_1=\psi(\xi,u)\tag{2}$ and $\dot\zeta=q_2(\zeta,y),\quad h_2=\phi(y,\zeta)\tag{3}$ whose dynamics are in general unmodeled. However, it is required that (2) has a linear structure (with an unknown Hurwitz matrix) and that the input/output behaviour of (3) satisfies suitable assumptions (in particular, the input/output gain is assumed to be known). The main contribution is an existence result for output dynamic feedback of the form $$\dot\chi=\varphi(y,\chi)$$, $$u=\theta(y,\chi)$$ which stabilizes the system for all the sufficiently small values of $$\mu$$.

##### MSC:
 93D21 Adaptive or robust stabilization 93C10 Nonlinear systems in control theory 93C41 Control/observation systems with incomplete information
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