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The history of linear matrix inequalities (LMIs) in the analysis of dynamical systems dates from over 100 years. The story begins around 1890 when Lyapunov published his work introducing what is now called the Lyapunov’s theory (Boyd et al., 1994). The researches and publications involving the Lyapunov’s theory have grown up a lot in recent decades (Chen, 1999), opening a very wide range for various approaches such as robust stability analysis of linear systems (Montagner et al., 2009), LMI optimization approach (Wang et al., 2008), H2 (Apkarian et al., 2001; Assuncao et al., 2007a; Ma & Chen, 2006) or H∞ (Assuncao et al., 2007b; Chilali & Gahinet, 1996; Lee et al., 2004) robust control, design of controllers for systems with state feedback (Montagner et al., 2005), and design of controllers for systems with state-derivative feedback (Cardim et al., 2009). The design of robust controllers can also be applied to nonlinear systems.

New Techniques for Optimizing the Norm of Robust Controllers of Polytopic Uncertain Linear Systems