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Homogeneous feedback stabilization. (English) Zbl 0736.93020
New trends in systems theory, Proc. Jt. Conf., Genoa/Italy 1990, Prog. Syst. Control Theory 7, 464-471 (1991).
Summary: [For the entire collection see Zbl 0726.00023.]
We address a special case of the general problem of finding continuous feedback laws (that lead to unique solutions) and asymptotically stabilize the origin of (in general) nonlinear smooth systems of the form (1) $$\dot x=f(x)+ug(x)$$ with $$x\in\mathbb{R}^ n$$, $$u\in\mathbb{R}$$. The purpose of this note is to further popularize the use of feedback laws that are $$\Delta$$-homogeneous (i.e. homogeneous w.r.t. a suitable family of dilations) for the global asymptotic stabilization of $$\Delta$$- homogeneous control systems, and for the local asymptotic stabilization of general nonlinear systems approximated by homogeneous systems.

##### MSC:
 93B52 Feedback control 93C15 Control/observation systems governed by ordinary differential equations 93C10 Nonlinear systems in control theory
##### Keywords:
continuous feedback laws; homogeneous systems
Zbl 0726.00023