Strong γkγk–γclH∞ stabilization with a new slack variable approach

This paper deals with the strong γkγk–γclH∞ 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 nnth order strong γkγk–γclH∞ stabilization. It is also proved that the design of an l×nl×nth order (l≥2l≥2) strong γkγk–γclH∞ controller can be transformed into that of an nnth order controller for an associated plant, which tackles the possible order problem. Furthermore, the H∞H∞ 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 to propose procedures for both nnth and l×nl×nth order controller designs. The effectiveness is indicated by several numerical examples.