This paper deals with a quadratic optimization problem for linear impulsive hybrid systems. We study a class of LQ-type impulsive hybrid optimal control problems (OCPs) and consider the application of the hybrid Maximum Principle (MP). Our aim is to investigate the natural relationship between the Pontryagin-type MP and the Bellman Dynamic Programming (DP) approach. As next we develop the “hybrid” Riccati formalism and discuss some related computational aspects. © 2010 AACC.