Overlapping quadratic optimal control of time-varying discrete-time systems

Overlapping quadratic optimal control of linear time-invariant systems and a commutative class of continuous-time, time-varying systems has been recently developed by using a generalized structure of complementary matrices. It has been shown that these structures offer a powerful and effective mean for decentralized control design for these classes of systems. In this paper, these structures are presented for general linear time-varying discrete-time systems. The results presented here concern the transition matrices and explicit conditions on complementary matrices for this class of systems. It essentially differs from continuous-time linear time-varying systems, where general results hold only for aggregations and restrictions. A guideline for their selection is given. The effectiveness of this generalized structure is illustrated by a numerical example of overlapping decentralized control design.