On strong γk-γcl H∞ stabilization and simultaneous γk-γcl H∞ control

The strong gamma_k-gamma_cl H_infin stabilization problem as well as the simultaneous gamma_k-gamma_cl H_infin control problem is addressed in this paper. Based on the bounded real lemma, a sufficient condition for strong gamma_k-gamma_cl H_infin stabilization is proposed, which leads to the design procedures that involve an algebraic Riccati equation and some LMI constraints. It is also proved that the simultaneous gamma_k-gamma_cl H_infin stabilization problem for r (r ges 2) plants is equal to strongly gamma_k-gamma_cl H_infin stabilize r-1 associated plants. Finally, a numerical example is presented to demonstrate the effectiveness of the result.