Interaction evaluation and decoupler design using Index of Interaction

Index of Interaction (IoI) proposed in [10] is a novel measure that allows a designer to relate the dynamic interaction in discrete time multivariable systems to the energy level of the discrete signals. In this paper, two objective measures of interaction called diagonal dominance and the worst case IoI are proposed. In comparison with the previously proposed measure [12], current measures provide a more comprehensive interaction evaluation scheme. In addition, they lead to a approximate decoupler design procedure which requires only solving of linear equations thereby making it much simpler to implement. Several examples are included to illustrate the procedures of interaction evaluation and design of an approximate decoupler based on diagonal dominance concept. Simulation study confirms that substantial improvement in dynamic interaction can be achieved by implementing the approximate decoupler designed.