H∞ control for buildings with time delay in control via linear matrix inequalities and genetic algorithms

This paper presents an H∞H∞ controller design approach for vibration attenuation of seismic-excited building structures with time delay in control input. The time delay is assumed to be uncertain time-invariant but has a known constant bound. Both of the state feedback and the static output feedback memoryless controllers can be designed to attenuate the system response due to disturbance on the controlled output to a prescribed level even when the time delay exists. The design approach is formulated in terms of the feasibility of certain delay-dependent matrix inequalities. The solution is found by combining the random search of genetic algorithms (GAs) and the solvability of linear matrix inequalities (LMIs). The performance of the presented control approach and the system stability when using this approach are demonstrated by numerical simulation results. It is confirmed that the presented approach may be a practical control strategy to be applied to seismic-excited building structures.