Stabilization Via Generalized Homogeneous Approximations

Abstract

We introduce a notion of generalized homogeneous approximation at the origin and at infinity which extends the classical notions and captures a large class of nonlinear systems, including (lower and upper) triangular systems. Exploiting this extension and although this extension does not preserve the basic properties of the classical notion, we give basic results concerning stabilization and robustness of nonlinear systems, by designing a homogeneous (in the generalized sense) feedback controller which globally asymptotically stabilizes a chain of power integrators and makes it the dominant part at infinity and at the origin (in the generalized sense) of the dynamics. Stability against nonlinear perturbation follows from domination arguments.

A homogeneous domination control method based on sampled‐data output feedback for lateral stability of an intelligent electric vehicle

“…Based on the homogeneous control theory, a kind of homogeneous domina-tion approach was proposed to obtain global output feedback stabilization for nonlinear systems without requiring the linear growth restriction of the nonlinear or uncertain terms [41][42][43][44]. Later, the homogeneous domination approach was developed further to cover more control systems and loosen the restriction in theory [45][46][47]. On the other hand, the homogeneous domination was studied and applied to the vehicle active suspension control system in engineering [48].…”