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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 \[ \dot\theta= f(y,t),\quad \dot x=Ax+Bu,\quad y=Cx+Du. \] The main purpose is to construct an input function \(u(t)\) which may depend on the fiber variable \(\theta\) 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 \(U(\alpha,t)\) which are periodic of period \(T\) with respect to \(t\). The function \(u(t)\) is defined according to the law \[ u(t)=U(\alpha_k,t)\quad\text{for }t\in [kT,(k+1)T] \] for a suitable choice of the sequence \(\{\alpha_k\}\).
The construction is valid under certain controllability-like assumptions on the \(\theta\)-subsystem.

MSC:

93D15 Stabilization of systems by feedback
93A99 General systems theory
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