Controlling grazing-induced multistability in a piecewise-smooth impacting system via the time-delayed feedback control

Abstract Grazing events may create coexisting attractors and cause complex dynamics in piecewise-smooth dynamical systems. This paper studies the control of grazing-induced multistability a soft impacting oscillator by using time-delayed feedback control. The switches from one to desired suppress near grazing events. We use path-following (continuation) techniques for non-smooth systems investigate robustness controller parameter dependence controlled system. In particular, several newly developed computational methods are used, including numerical method analysing delay equations calculating Lyapunov exponents point estimation. Numerical simulations demonstrate that delayed is effective, proper selection gain time can simplify system grazing.