Controllability and dissipativity analysis for linear systems with derivative input

This paper investigates controllability and dissipativity analysis problem for linear systems with derivative input. First, we show that linear systems with derivative input can be changed into special class of singular systems. A necessary and sufficient condition for the controllability of linear systems with derivative input is derived. Second, a necessary and sufficient condition for the dissipativity of this type of linear systems with quadratic form storage function is derived using the linear matrix inequality approach. Based on this condition, the dissipativity of singular systems with impulse behavior is investigated and a parametrization for all possible solutions on dissipativity is presented. Finally, two examples are given to show the validity of the derived results.