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Output feedback disturbance decoupling in nonlinear systems. (English) Zbl 0863.93039
The paper deals with the disturbance decoupling problem under (dynamic) output feedback for nonlinear systems. That is, systems of the form $$\dot x=f(x) + g(x)u + d (x)q$$, $$y= h(x)$$ and $$z= k(x)$$, with $$x\in \mathbb{R}^n$$, $$u\in \mathbb{R}^m$$, $$y\in \mathbb{R}^p$$, $$z\in \mathbb{R}^s$$ and $$q\in \mathbb{R}^t$$ are considered and the goal is to find a dynamic output feedback $$\dot \eta = \gamma (\eta,y,v)$$, $$u= \alpha (\eta,y,v)$$ with $$\eta\in \mathbb{R}^n$$ such that for the closed loop dynamics the output $$z$$ is completely independent of the disturbance $$q$$, no matter what the new inputs $$v$$ are. Some partial results on this problem are obtained by using a linear algebraic framework involving, among others, a characterization of conditioned invariant codistributions. This concept is a generalization of the more common conditioned invariant distributions where usually involutivity of the distribution is required.

##### MSC:
 93B52 Feedback control 93B29 Differential-geometric methods in systems theory (MSC2000) 93C73 Perturbations in control/observation systems 93C10 Nonlinear systems in control theory
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