Local stability for a class of piecewise affine Filippov systems

In this paper the local asymptotic stability problem is investigated for a class of piecewise affine (PWA) Filippov systems. We address a particular case of PWA systems with linear switching surfaces crossing at an equilibrium resulting from sliding dynamics (Filippov/pseudo equilibrium). The PWA systems may also present other unstable equilibria. Sufficient Lyapunov-based conditions are given for characterising the local asymptotic stability of the Filippov equilibrium. Methods are proposed to estimate the domain of attraction.