Stability analysis of discontinuous dynamical systems using vector Lyapunov functions (Q1582331)

The paper considers some development of discontinuous systems of differential equations \[ \dot x= g(x,t),\quad \tau_k\leq t\leq \tau_{k+1}, \] \[ x(\tau_{k+ 1})= \lim_{t\to \tau_{k+1}-0} h(x(t), t),\quad k=0,1,2,\dots \] each set of discontinuities being associated to some solution. Basic notions of stability are revised. The method of the vector Lyapunov functions is applied to obtain stability theorems for interconnected systems. Stability conditions are given in terms of \(M\)-matrices. Two examples are discussed.