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Hybrid feedback laws for a class of cascade nonlinear control systems. (English) Zbl 0862.93048

The authors consider systems of the form

θ ˙=f(y,t),x ˙=Ax+Bu,y=Cx+Du·

The main purpose is to construct an input function u(t) which may depend on the fiber variable θ and such that the system becomes asymptotically stable at the origin when u is replaced by u(t).

The construction involves a family of functions U(α,t) which are periodic of period T with respect to t. The function u(t) is defined according to the law

u(t)=U(α k ,t)fort[kT,(k+1)T]

for a suitable choice of the sequence {α k }.

The construction is valid under certain controllability-like assumptions on the θ-subsystem.

MSC:
93D15Stabilization of systems by feedback
93A99General systems theory