Multiobjective L₁/H_∞ controller design for systems with frequency and time domain constraints

We develop an optimal mixed-norm L₁ bound/H_∞ controller synthesis framework for continuous-time linear systems. This multiobjective problem is treated by forming a convex combination of both L₁ (time domain worst-case peak amplitude response) and entropy (frequency domain worst-case H_∞ disturbance attenuation) performance measures. For flexibility in controller synthesis, we adopt the approach of fixed-structure controller design which allows consideration of arbitrary controller structures, including order, internal structure, and decentralization. Finally, using a quasi-Newton continuation algorithm, we demonstrate the effectiveness of the proposed mixed-norm L₁/H_∞ approach via a numerical design example