Optimal sensor and actuator location for descriptor systems using generalized Gramians and balanced realizations

This work presents two methods for optimal sensor and actuator location for linear time-invariant descriptor systems. The objective is the improvement of the state controllability and state observability. Since these two notions are quantified by the corresponding Gramians, the optimal location is based on the maximization of the generalized Gramians. Firstly, a method aims at maximizing the energy provided by the inputs to the system and the energy collected by the outputs. Secondly, state controllability and state observability are jointly improved by considering a balanced realization of descriptor systems. Finally, sensor location is exploited for disturbance decoupling. A numerical example illustrates the efficiency of the proposed methods.