Controllability, Observability and Observers

Abstract

The concepts of system observability and controllability are important aspects of state-variable analysis and design. In general terms, a system is said to be controllable if it can be driven to an arbitrary state by an applied input and, conversely, is uncontrollable if it is not possible to reach an arbitrary state. A system is said to be observable if the state x can be deduced from measurements on the available output y, and if the state cannot be deduced from y the system is unobservable. In the context of natural modes, controllability implies that all modes can be excited (controlled) from the input, and observability implies that any mode excited can be detected (observed) in the output y. In the theoretical investigation of controllability and observability, the rank of a matrix is an essential concept, and is considered in appendix 2. The final sections of this chapter introduce the principles of observers, which are used to provide an estimate of missing state information.