A linear quadratic tracking problem for impulsive controlled stochastic systems: The infinite horizon time case.

We investigate a linear quadratic tracking problem for impulsive controlled stochastic systems. The main tool in the derivation of the optimal control is the stabilizing solution for a class of backward jump matrix linear differential equation. We introduce the concept of mean square stability by impulses and consider the properties of stabilizing solution of the associated backward jump matrix linear differential equation with Riccati‐type operators. Necessary and sufficient conditions that guarantee the existence of the unique optimal control for the linear quadratic tracking problem for impulsive controlled stochastic systems are proved. [ABSTRACT FROM AUTHOR]