Quadrature path-counting method for the disturbance decoupling problem in linear multivariable systems

The disturbance decoupling problem for a linear multivariable control system is reformulated in terms of a summation over possible propagation paths of a disturbance through the network of system variables. Each path is classified according to the number of time integrations (quadratures) it contains. The resulting formulation of the equations for the control coefficients is easier to follow than more formal algebraic approaches, in that there is a more direct physical interpretation of the terms involved. The method applies also to discrete-time systems for sufficiently slow disturbances.