ℓ1-Optimal control with asymmetric bounds

In this paper a novel way to handle the analysis and design of control systems with bounded asymmetrical signals is presented. Instead of the standard peak-to-peak norm, normally used in ℓ1-optimal control, this paper propose to use an asymmetric objective functional, which simplifies the consideration of asymmetrically bounded signals. Necessary and sufficient conditions are derived to check if some performance specifications, expressed using this objective functional, are fulfilled. The analysis and the synthesis problems are also formulated with respect to this objective functional: As in the standard ℓ1-optimal control, this approach leads to a linear programming problem which can be solved by off-the-self tools.