Elimination of Expensive Sensors in Static State Feedback Control with Specified Transient Behaviour

This article considers the problem of designing a static feedback control for a linear time invariant system such that a specified set of expensive sensors, used for state measurements, are eliminated. If a particular column of the feedback gain matrix is entirely zero, then the state corresponding to that column is not required to be measured, and hence, the corresponding sensor can be eliminated. With this observation, a structured feedback gain matrix is designed where the columns, corresponding to the specified expensive sensors, are made entirely zero. The desired transient behaviour is achieved by assigning the poles of closed loop system in a suitably chosen region in the left half of the complex plane. A linear matrix inequality (LMI) feasibility problem is formulated to compute the desired gain matrix. The developed methodology is demonstrated with practical examples.