An invariance principle for discontinuous dynamic systems with application to a Coulomb friction oscillator

An invariance principle for a class of ordinary differential equations with discontinuous right-hand side is developed. Based on this principle, asymptotic stability of one-degree-of-freedom mechanical oscillators which Coulomb friction is studied. The system is shown to be asymptotically stabilizable via a static feedback of the position, unlike those systems with no friction, whose stabilization requires a dynamic feedback when the position is the only available measurement. Along with this development, a velocity observer is proposed. Theoretical results of the paper are supported by some numerical simulations which, in addition, carry out a finite-time convergence of the controller and the observer proposed. [S0022-0434(00)00804-2].