Quantitative measures of compensation capabilities and output noise sensitivities of linear systems

Controllability and observability are a structural property that carries information useful for control system design. There are many measures to determine the location of actuator and sensor like degree of controllability (DOC), degree of observability (DOO) and degree of disturbance rejectability(DODR). However, for a system which uses both actuators and sensor, the placement of actuator can be affected by the placement of sensor and vice versa. Therefore, the measure which can consider both controllability and observability simultaneously is proposed in this paper and it is called degree of compensation capability (DOCC) and degree of output noise sensitivity (DONS). DOCC is sum of the three measures of DOC, DOO and DONS. DONS is affected by the both magnitude and direction of the controllability and observability gramians. Numerical example is shown to demonstrate the usefulness of the proposed measures.