Stability of equilibria of some switched non-linear systems with applications to control synthesis for electrohydraulic servomechanisms

Stability of the zero solution is analyzed for a family of switched systems indexed by a parameter, each system having λ = 0 in the spectrum of the Jacobian matrix calculated in zero. It is proved that existence of a common quadratic Lyapunov function for some lower dimensional linear systems is sufficient to ensure local uniform stability of the zero solution of the switched non-linear system and a regular asymptotic behaviour. An application to control synthesis for stabilizing equilibria in a switched non-linear control system modelling an electrohydraulic servomechanism is given.