Some New Results on Strong $\gamma _k$ - $\gamma _{cl} H_{\infty }$ Stabilization

The strong gamma_k-gamma_cl H_infin stabilization problem is addressed in this paper. Based on the bounded real lemma, an improved sufficient condition on strong H_infin stabilization as well as its dual form is derived, which extends the ARE constraint in the former results into an inequality constraint. Two path-following algorithms are proposed to solve the associated optimization problems with BMI constraints, which lead to full order controllers. A numerical example is presented to demonstrate the effectiveness of the result.