Existence and stability of limit cycles in a delayed dry-friction oscillator

Periodic, chaotic, chattering, and bifurcation behavior are fundamental consequences of the nonsmooth nature of systems with dry friction. This work is concerned with the analysis of a single degree of freedom system which is additionally damped by a delayed dry friction device. We get a complete set of closed-form expressions to describe the dynamics of the delay-induced phenomena exhibited by the system. The conditions to determine the existence and stability of limit cycles are clearly defined. This analysis is addressed in the context of both classic stability theory for nonlinear systems and the qualitative theory of Piecewise Smooth Dynamical Systems. Through exhaustive numerical simulations the effectiveness of the set of closed-form expressions is confirmed. Excellent agreement was found between the numerical and analytical results.