Linear quadratic optimal control for linear implicit system

This paper considers the linear quadratic optimal control problem for linear implicit systems based on the dissipation inequality. We derive a necessary and sufficient condition for the dissipativeness with respect to a quadratic supply rate in terms of a linear matrix inequality (LMI) condition with an equality constraint. Based on this constrained LMI condition, the optimal control law is given by an implicit algebraic constraint among system variables. We also show that the present constrained LMI condition easily reduces to an LMI without any equality constraints.