Decoupling of Discrete-time Dynamical Systems Through Input-Output Blending

Abstract

This paper presents a subsystem decoupling method for Linear Time Invariant Discrete-time systems. The aim is to control a selected subsystem, while not affecting the remaining dynamics. The paper extends earlier continuous time results to discrete time systems over a finite frequency interval. Decoupling is achieved by suitable input and output blend vectors, such that they maximize the sensitivity of the selected subsystem, while at the same time they minimize the transfer through the undesired dynamics. The proposed algorithm is based on an optimization problem involving Linear Matrix Inequalities, where the H- index of the controlled subsystem is maximized, while the transfer through the dynamics to be decoupled is minimized by a sparsity like criteria. The present approach has the advantage that it is directly applicable to stable and unstable subsystems also. Numerical examples demonstrate the effectiveness of the method.