Causal stabilisation of strictly causal multidimensional discrete objects
Efim N. Rosenwasser, Wolfgang Drewelow, Torsten Jeinsch · International Journal of Control · 2022
The paper presents a solution to the problem of constructing the set of causal discrete controllers for strictly causal multidimensional discrete objects based on the application of determinant polynomial equations (DPE). It is shown that the properties of the solutions of the corresponding DPE depend on the type of the mathematical description of the controlled object. If the object is described by a backward polynomial model in terms of the B-shift operator ζ, it is shown that the corresponding DPE generates only causal solutions. This allows us to construct a parameterisation of the set of transfer matrices of causal stabilising controllers in a form that corresponds to the multidimensional Youla-Kučera parameterisation. For the case where the object is given as a forward polynomial model in the F-shift operator z, special techniques are developed to extract the set of all stabilising controllers from the subset of causal solutions.