Switching Gains for Semiactive Damping via Nonconvex Lyapunov Functions

Gain switching is proven to be an effective technique for semiactive damping of vibrating structures. Typically, switching control is based on convex, in particular quadratic, Lyapunov functions, which impose conservative solutions. In this brief we propose a switching technique based on ad hoc nonconvex Lyapunov functions, recently introduced in the literature. Remarkable advantages can be shown by considering well-known criteria such as L₂ and H_∞. We propose a switching strategy based on the minimum of quadratic Lyapunov functions and we show that such a strategy outperforms the effect achieved with the optimal constant gain. Explicit bounds can be assured. The scheme is amenable for implementation as very simple tools such as Lyapunov and Riccati equations are involved. Results are also validated by simulations of a realistic building structure under seismic action, based on the recorded data of the El Centro earthquake.