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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 \(\sigma_ 1\) and \(\sigma_ 2:\dot x_ 1=A_ 1x_ 1b_ 1u,\quad \sigma_ 1=c^ T_ 1x_ 1,\quad x_ 1(0)=x_{10}\) \[ \dot x_ 2=A_ 2x_ 2+b_ 2u,\quad \sigma_ 2=c^ T_ 2x_ 2,\quad x_ 2(0)=x_{20}, \]
\[ u(t)=-\phi (\sigma_ 1(t)+\sigma_ 2(t)), \] where \(A_ i\), \(c_ i\), \(b_ i\) are \(n_ i\times n_ i\) real matrices and \(n_ i\)-vectors, respectively \((i=1,2)\); \(x_ i\) \((i=1,2)\) are the state vectors and \(\phi\) 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

MSC:

93D10 Popov-type stability of feedback systems
34D99 Stability theory for ordinary differential equations
93A15 Large-scale systems
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References:

[1] Ch J., Méthodes d’étude des Syslémes Asservis Non-Linéaires (1967)
[2] POPOV V. M., Automn remote Control 24 (1963)
[3] DOI: 10.1049/piee.1970.0366 · doi:10.1049/piee.1970.0366
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