A linear matrix inequality approach to synthesizing low order mixed l1/Hp controllers

Mixed objective control problems have attracted much attention since they allow for capturing different performance specifications without resorting to approximations or the use of weighting functions, thus eliminating the need for trial and error type iterations. The paper addresses the problem of designing stabilizing controllers that minimize the l₁ norm of a certain closed-loop transfer function, while maintaining the H₂ norm (mixed l₁/H₂), or the H_∞ norm (mixed l₁/H_∞), of a different transfer function below a prespecified level. Based on a linear matrix inequality approach, the main results of this paper show that, suboptimal controllers can be synthesized by a two-stage process, involving an LMI optimization problem and a line search over (0, 1). Furthermore, this approach also provides an LMI-based parameterization of all suboptimal-output feedback controllers, including reduced order ones, for mixed l₁/H_∞ and l₁/H₂ problems