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Displaying similar documents to “A new kind of augmentation of filtrations”

On the -stabilization of the double integrator subject to input saturation

Yacine Chitour (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a finite-dimensional control system ( Σ ) x ˙ ( t ) = f ( x ( t ) , u ( t ) ) , such that there exists a feedback stabilizer that renders x ˙ = f ( x , k ( x ) ) globally asymptotically stable. Moreover, for with an output map and 1 p q , we assume that there exists a 𝒦 -function such that H ( x u ) q α ( u p ) , where is the maximal solution of ( Σ ) k x ˙ ( t ) = f ( x ( t ) , k ( x ( t ) ) + u ( t ) ) , corresponding to and to the initial condition . Then, the gain function G ( H , p , q ) of given by 14.5cm G ( H , p , q ) ( X ) = def sup u p = X H ( x u ) q , is well-defined. We call profile of for any 𝒦 -function which is of the same order of magnitude...