an:03856949
Zbl 0538.93048
Djordjevic, Milorad Z.
Stability analysis of large scale systems whose subsystems may be unstable
EN
Large Scale Syst. 5, 255-262 (1983).
00148819
1983
j
93D05 93A15 93C10 93C15 34D20
nonlinear, stationary, interconnected systems; Lyapunov functions
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.
D.A.Wilson