Trade-off between the H2 and H∞ in the multi-objective state feedback synthesis through LMI characterizations

The mixed performance and robustness of control problems have been the object of much attention. These various objective problems are rarely encompassed by a single synthesis criterion. While some tracking and robustness are best captured by the H_∞ criterion noise insensitivity is more naturally expressed in H₂ terms, and transient behaviors are easily tuned in terms of L₁ norms or closed loop damping. We present a methodology for designing mixed L₁/H₂/H_∞ controllers for MIMO systems through linear matrix inequalities (LMI) techniques. These controllers allow for minimizing the worst case peak output due to disturbances and noise, and acquire robust pole placement by satisfying multi-objective criteria. A physically motivated example is given to demonstrate the effectiveness of the mix-controller for mix performance and robustness.