Optimal H∞ output feedback control systems with time delay

An H-infinity direct output feedback control algorithm through minimizing the entropy, a performance index measuring the tradeoff between H-infinity optimality and H-2 optimality, is developed in this paper to reduce the earthquake response of structures. To achieve optimal control performance and assure control system stability, the strategy to select both control parameters gamma and alpha is extensively investigated considering the control force execution time delay. It is found that a lower bound of gamma and an upper bound of alpha exist. The selection beyond these values will cause the control system instability. For a damped structure, analytical expressions of direct output feedback gains, controlled frequencies and damping ratios are derived. It can be proved that the conventional LQR control is a special case of the developed H-infinity control. In real active control, control force execution time delay cannot be avoided. This paper gives explicit formulas of maximum allowable delay time and critical control parameters for the design of a stable control system. Some solutions are also proposed to lengthen maximum allowable delay times.