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Stability of composite systems with an asymptotically hyperstable subsystem. (English) Zbl 0606.93059

The system consists of two finite-dimensional linear subsystems described by state-space equations with scalar input u and outputs σ 1 and σ 2 :x ˙ 1 =A 1 x 1 b 1 u,σ 1 =c 1 T x 1 ,x 1 (0)=x 10

x ˙ 2 =A 2 x 2 +b 2 u,σ 2 =c 2 T x 2 ,x 2 (0)=x 20 ,
u(t)=-ϕ(σ 1 (t)+σ 2 (t)),

where A i , c i , b i are n i ×n i real matrices and n i -vectors, respectively (i=1,2); x i (i=1,2) are the state vectors and ϕ is a real-vaued continuous function. One of the two subsystems is assumed to be hyperstable. Under some additional assumptions stability properties of the composite system are studied.

Reviewer: L.Faibusovich
93D10Popov-type stability of feedback systems
34D99Stability theory of ODE
93A15Large scale systems