Djordjevic, Milorad Z. Stability analysis of large scale systems whose subsystems may be unstable. (English) Zbl 0538.93048 Large Scale Syst. 5, 255-262 (1983). A method is proposed for studying the stability of nonlinear, stationary, interconnected systems. In particular the case is considered of two interconnected systems in the form \(\dot x_ i=f_ i(x_ i)+g_ i(x_ i,x_ 2),\quad i=1,2.\) Lyapunov functions are constructed for the individual systems (i.e. with \(g_ i=0)\), together with a function \(v_{12}(x_ 1,x_ 2)\) representing ”energy coupling” between the subsystems. A weighted sum of these functions is taken as a candidate for a Lyapunov function for the full system, and a sufficient condition is obtained for system stability. A method for constructing \(v_{12}\) is suggested and the technique is illustrated with two examples. Reviewer: D.A.Wilson Cited in 1 ReviewCited in 13 Documents MSC: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 93A15 Large-scale systems 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations 34D20 Stability of solutions to ordinary differential equations Keywords:nonlinear, stationary, interconnected systems; Lyapunov functions PDF BibTeX XML Cite \textit{M. Z. Djordjevic}, Large Scale Syst. 5, 255--262 (1983; Zbl 0538.93048)