Overlapping quadratic optimal control of linear time-varying commutative systems

Overlapping quadratic optimal control of linear time-invariant continuous-time systems by using generalized selection of complementary matrices has been recently developed as a powerful and effective mean for decentralized control design of linear time-invariant systems. In this paper, it is shown that similar generalizations exist for linear time-varying systems. The results presented here concern implicit conditions for a general form of the transition matrices and explicit conditions for a commutative class of linear time-varying systems.