Strong γ k – γ c l H ∞ stabilization with a new slack variable approach

• Published in: Automatica (Oxford) 2009-08, Vol.45 (8), p.1861-1867
• Main Authors: Cheng, Peng, Cao, Yong-Yan, Sun, Youxian
• Format: Article
• Language: English
• Subjects: [formula omitted] control; Bilinear matrix inequality (BMI); Bounded real lemma; Linear matrix inequality (LMI); Strong stabilization
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2009.03.024

This paper deals with the strong γ k – γ c l H ∞ 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 γ k – γ c l H ∞ stabilization. It is also proved that the design of an l × n th order ( l ≥ 2 ) strong γ k – γ c l H ∞ controller can be transformed into that of an n th order controller for an associated plant, which tackles the possible order problem. Furthermore, the 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 n th and l × n th order controller designs. The effectiveness is indicated by several numerical examples.