Decentralized control synthesis using orthogonal functions

In this paper, a new technique of decentralized control synthesis is proposed by using orthogonal functions. This approach is based on the transformation of the state differential equation of the dynamic system into an algebraic equation, derived from the projection of the system variables on an orthogonal basis and the using of the operational properties of the considered orthogonal functions, and especially the operational matrix of integration. The developed method leads to the determination of decentralized control gains such that each controlled subsystem of the global system has the desired performances of a chosen reference model.