On the input-to-state stabilization of affine systems

The article examines the possibility of global stabilization of affine systems of arbitrary dimension with the scalar control and scalar disturbance. In this case the corresponding systems without disturbances are equivalent to regular systems of a canonical form. We obtain easily verifiable conditions implying that Lyapunov function built on the basis of the regular canonical form for the system with control is Lyapunov function for the system with disturbances. We provide the research with the results of numerical modeling of the stabilization process for three-dimensional affine systems with disturbances.

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