Multiobjective L1/H∞ Controller Design for Systems with Frequency and Time Domain Constraints

Abstract

In this paper we develop an optimal mixed-norm L1 bound/H∞ and l1 bound/H∞ controller synthesis framework for continuous-time and discrete-time systems. This multiobjective problem is treated by forming a convex combination ofboth 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 fixedstructure 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 two numerical design examples.