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A geometric approach to nonlinear singularly perturbed control systems. (English) Zbl 0633.93033
The paper considers a class of nonlinear control systems depending on a parameter $dz/dt=Z(z,\epsilon,u)$. A necessary and sufficient condition including “conservation”, “equilibrium” and “transversality” properties is presented under which the system can be transformed into a singular perturbation system $dx/d\tau =\epsilon X(x,y,\epsilon,u)$, $dy/d\tau =Y(x,y,\epsilon,u)$ such that $\{$ (x,y), $Y(x,y,0,u)=0\}$ is a smooth control-dependent manifold of constant dimension. As examples a point-mass model of an aircraft and a model of a manipulator with flexible joints are discussed.
Reviewer: A.Dontchev

##### MSC:
 93C10 Nonlinear control systems 93B27 Geometric methods in systems theory 34E15 Asymptotic singular perturbations, general theory (ODE) 70Q05 Control of mechanical systems (general mechanics) 93C15 Control systems governed by ODE 93C95 Applications of control theory
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