Overlapping Quadratic Optimal Control of Linear Time-Varying Commutative Systems

Abstract

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 means of 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. Several important large classes of complementary matrices are selected to offer computationally attractive results. The effectiveness of this generalized selection scheme is illustrated by a numerical example of overlapping decentralized control design.