On initial jumps for singular systems in connection with LQ optimal control

This paper is concerned with the connection between optimal state feedback gains and initial jumps for the linear quadratic optimal control problem involving singular systems. It is known that the optimal state feedback gain for such an optimal control problem is not unique. Thus, different optimal gains lead to different closed-loop systems. In this paper, it is pointed out that all such optimal closed-loop systems will generically have jumps and these initial jumps are always the same. More importantly, a set of conditions under which LQ optimal gains will yield no initial jumps in the closed-loop systems is derived.