Active Vibration Control for Uncertain Time-Varying Systems Via Output Feedback

This work applies the developed Lyapunov method to the design of active vibration control laws for uncertain time varying systems, which are described via linear differential inclusions. The design objective is to suppress the steady state output response to a class of sinusoidal and periodic disturbances via output feedback. As shown in a work (T. Hu et al., 2005), the L ₂ gain for a linear differential inclusion is no longer a valid upper bound for the steady state gain from sinusoidal disturbances to the output. Instead, a Lyapunov approach was developed in (T. Hu et al., 2005) for the evaluation of the steady-state gain. Based on this Lyapunov approach, we derive an LMI-based algorithm for the construction of output feedback laws for the suppression of the steady-state output response. A numerical example demonstrates the effectiveness of the design algorithm.