A linear matrix inequality approach to synthesizing low order l1 controllers

The l¹ control theory is appealing, since it allows for directly incorporating time-domain specifications into the controller synthesis procedure and furnishes a complete solution to the robust performance problem. Moreover, in the SISO case, the synthesis procedure can be recast into a finite-dimensional linear programming problem and solved efficiently. The MIMO case can be solved iteratively by adding fictitious inputs and outputs to recast the problem into an one-block form. However, it is well known that, in contrast to the H₂ and H_∞ cases, optimal l¹ controllers can have arbitrarily high order, even when the states of the plant are available for feedback. In this paper, we address the problem of designing low order suboptimal l¹ controllers using a linear matrix inequality (LMI) optimization approach. The main results show that, in the state-feedback case, the suboptimal controller is static, while in the output-feedback case it has the same order as that of the plant. In both cases the synthesis process involves solving an LMI feasibility problem and a scalar minimization over (0,1)