Strong γk-γcl H∞ stabilization with a new slack variable approach

For the strong gamma_k-gamma_cl H_infin stabilization problem, a new bounded real lemma is provided by adding two slack variables, which provides extra freedom to include more control constraints in handling robust control problems. With the extended bounded real lemma, a new sufficient condition is proposed for n-th order strong gamma_k-gamma_cl H_infin stabilization. Furthermore, the H_infin stable stabilization and strong stabilization problems can also be solved by relaxing certain constraints accordingly. Despite the BMI constraints, the path-following and alternative iteration methods are adopted for the controller design. The effectiveness of the algorithms is indicated by a numerical example.