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The strong gammak-gammacl Hinfin stabilization problem is addressed in this paper. Based on the bounded real lemma, an improved sufficient condition on strong Hinfin 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.