Optimal sensor/actuator location for descriptor systems using Lyapunov-like equations

A method for optimal sensor and actuator location is proposed for the linear time-invariant descriptor systems. The actuators are selected to minimize the input energy needed to reach a given state and the sensor are selected to maximize the energy transmitted from the state variables to the outputs. Since controllability and observability can be quantified by the corresponding gramians, the problem of optimal actuator and sensor location is linked to the maximization of the gramians. Due to the finiteness of the possible locations for actuators and sensors this problem can be efficiently solved by using integer optimization tools. An illustrative example is provided.