Sensitivity Synthesis for MIMO Systems: A Multi Objective Nm Approach'

Abs t r ac t A series of multi objective 31, design problems are con-sidered in this paper. The problems are formulated as a number of coupled '?fm design problems. These 31, problems can be formulated as sensitivity prob-lems, complementary sensitivity problems, or control sensitivity problems for every output (or input) in the system. It turns out that these multi objective E, de-sign problems, based on a number of different types of sensitivity problems, can be exactly decoupled into k 31, sensitivity problems for stable systems, where k is the number of outputs (for unstable systems, indepen-dent stabilization is required). 1. Introduct ion The area of robust control has received tremendous at-tention in the control literature recently. Especially, 31, theory has been in the focus since its breakthroughs during the 1980's. In the main, 31, control is motivated by the following two applications. First, if the modeling errors are as-sumed to be bounded in 31, norm by a known bound, bounding a transfer function determined by the plant and the controller in 31, norm guarantees robust sta-bility. Second, formulating optimality conditions as fre-quency domain bounds for a number of transfer func-tions, 31, theory can be applied as a loopshaping tool. In some cases, robust stability suffices, but in most ap-plications it is required to satisfy some memure of op-timality, and hence some kind of loopshaping technique has to be employed. In the mainstream literature, it is suggested to use 31, theory for such purposes by stacking control objectives as, e.g., in the so called mixed sensitivity approach, where a design criterion of the form is considered, where S (.) and T (.) are the closed loop serisitivity and complementary sensitivity, and Ws (.