Sensor placement in LTI systems with poly topic uncertainty via convex optimization

In this paper, the problem of sensor placement in linear time-invariant systems subject to polytopic uncertainty is considered. The main objective is to design a fixed-order controller to obtain a satisfactory H_∞ performance with minimum number of sensors. The problem is formulated as an optimization problem based on the minimization of the cardinality of a special matrix of the controller subject to some H_∞ constraints. Then, the problem is approximated to a convex optimization by means of some slack matrices and the relaxation of cardinality by an iterative weighted l₁ norm. The proposed approach is applied to the problem of phasor measurement unit placements in IEEE 14-bus test system.