Delay-Independent Stability of a Tri-stable Energy Harvesting System with Time-Delayed Feedback Control

This paper analyzes the delay-independent stability and harvesting performance of a tri-stable vibrational energy harvester (TVEH) with time-delayed feedback control. The dynamical model of the controlled electromechanical TVEH is established, and the method of multiple scales is employed to derive the steady-state response near the primary resonance. The delay-independent stability conditions of the TVEH are obtained using Routh Hurwitz criterion and classical Sturm criterion. The influences of time-delayed feedback control on the TVEH's output and jump phenomena are discussed through the steady-state response. Furthermore, appropriate choices of feedback gains and time delays can ensure the system stability and enhance the output power. The theoretical results are validated through numerical simulations, demonstrating the effectiveness of the proposed control strategy.