Examples of extreme cases in l1 and H∞ optimization

Advances in the theory of robust control have brought forth two methodologies for controller design: l₁ and H_∞ . In this paper the authors take the approach of using examples to illustrate some tradeoffs while designing controllers using either of the two methodologies. Further, for the sake of simplicity the authors consider the case of minimization of the sensitivity transfer function in all the examples. First, the authors discuss the frequency domain properties of l₁ optimal solutions and compare them with H _∞ optimal solutions. Next the authors contrast l₁ and H_∞ optimal solutions and explore their extreme behavior. Finally with the help of an example the authors illustrate some interesting properties of mixed minimization