The stability analysis on model following LSS and the time-varying weighted sum method (Q807816)

Stability of composite systems of the form \[ \frac{dx_ i}{dt}=\phi_ i(x_ i,t)+p_ i(x_ i,...,x_ N,t),\quad x_ i\in {\mathbb{R}}^{m_ i} \] are studied by the use of Lyapunov functions and m-matrices. A weighted sum V()\(=\sum^{N}_{i=1}d_ i(t)v_ i()\) of subsystem Lyapunov functions is used and a certain connection matrix is assumed to be an M-matrix. The asymptotic stability in the large of the equilibrium point is then proved.