New dilated LMI characterizations for continuous-time multiobjective controller synthesis

This paper provides new dilated linear matrix inequality (LMI) characterizations for continuous-time controller synthesis. The dilated LMIs enable us to parametrize controllers without involving the Lyapunov variables in the parametrizations. Taking advantage of this feature, we can readily design multiobjective controllers with non-common Lyapunov variables, whereas we are forced to employ a common one in the well-known Lyapunov shaping paradigm. In particular, it is shown that the proposed dilated-LMI-based approach to H₂/D-stability synthesis encompasses the corresponding Lyapunov shaping paradigm as a special case. In this sense, the results of this paper can be viewed as partial counterparts of those obtained in the discrete-time setting.