Quantitative Measures of output noise sensitivities of linear systems in modal domain

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 defined and it is called degree of compensation capability(DOCC) and degree of output noise sensitivity(DONS). DONS is a measure that represents the effect of output noise to control input and it can be represented by the inverse of the product of controllability and observability Gramian. DONS is applied to the modal domain system in this paper and numerical example is shown to demonstrate the usefulness of the proposed measures.