Delay-independent stability of moments of a linear oscillator with delayed state feedback and parametric white noise

• The delay-independent stability of a linear delayed system with parametric noise is studied.
• The delay-independent stability criteria of system moments are proposed.
• The delay-independent stable regions are plotted in the parameter space of concern.
• The proposed criteria are valid for both short and large time delays.

The stability of a linear oscillator with delayed state feedback driven by parametric Gaussian white noise is studied in this paper. The first and second order moment equations of the system response are derived by using moment method and Itô differential rule. Based on the moment equations, the delay-independent stable conditions of both moments are proposed: For the first order moment, the sufficient and necessary condition that guarantee delay-independent stability is identified to that of the deterministic system; for the second order moment, the sufficient condition that ensure delay-independent stability depends on noise intensity. The theoretical results are also illustrated with numerical simulations.