Achievable closed-loop properties of systems under decentralized control: conditions involving the steady-state gain

The question of the existence of decentralized controllers for open-loop stable multivariable systems which provide particular closed-loop properties is investigated. In particular, we study the existence of decentralized controllers which provide integral action (Type I closed-loop performance) and also demonstrate one or more of: unconditional stability, integrity with respect to actuator and sensor failure, and decentralized unconditional stability. Necessary, sufficient, and, in some cases, necessary and sufficient conditions on the open-loop steady-state gain are derived such that there exists a controller which provides these desired closed-loop characteristics. These results provide the basis for a systematic approach to control structure selection for decentralized controller design