A New Extended LMIs Approach for Continuous-time Multiobjective Controllers Synthesis

A new linear matrix inequality (LMI) characterizations for continuous-time system is presented. This new proposed procedure relies on the introduction of new extra variables and enables us to parametrize controllers without involving the Lyapunov variables in parametrizations. Taking advantage of this feature, we can use different Lyapunov functions to deal with the multiobjective control problem with non-common Lyapunov variables, and reduce the conservation under the usual existing standard conditions for the multiobjective control problem based on LMI. The numerical simulations demonstrates the validity of this design framework