Use of kernels of bicausal operators in scalar gain-phase predictive control

The implementation of the decomposition of linear discrete-time multivariable problems through either singular values/principal directions, or eigenvalues/eigenvectors is inherently anticausal. One way to avoid this is to introduce a ´pseudodelay´ into the controller, but this is undesirable. Here the problem is examined in the scalar case, and a new algorithm proposed which deploys a kernel to characterise all the available degrees of freedom, and thus overcome completely the problems of delay and anticausality.