State deadbeat response and observability in multi-modal systems

Two aspects of multimodal systems are examined. It is shown that any completely controllable system with state dimension n not exceeding three allows a choice of feedback matrices resulting in a state deadbeat response. Some of the results presented here are valid for arbitrary n, and it is suggested that for all n the state deadbeat response can be obtained under the hypothesis of complete controllability. The controllability canonical form for a multimodal system is refined by introducing a notion of observability which is dual to controllability for these systems.