State feedback stabilization of linear time-varying systems on time scales

A fundamental result in linear system theory is the development of a linear state feedback stabilizer for time-varying systems under suitable controllability constraints. This result was previously restricted to systems operating on the continuous (¿) and uniform discrete (h¿) time domains with constant step size h. Using the framework of dynamic equations on time scales, we construct a linear state feedback stabilizer for time-varying systems on arbitrary time domains.