de la Sen, M. Stability of composite systems with an asymptotically hyperstable subsystem. (English) Zbl 0606.93059 Int. J. Control 44, 1769-1775 (1986). 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 Cited in 10 Documents MSC: 93D10 Popov-type stability of feedback systems 34D99 Stability theory for ordinary differential equations 93A15 Large-scale systems Keywords:hyperstability; scalar input; composite system PDFBibTeX XMLCite \textit{M. de la Sen}, Int. J. Control 44, 1769--1775 (1986; Zbl 0606.93059) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.