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

It is known that the linear quadratic optimal state feedback gain for singular systems 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.