The use of symbolic computation for the problem of stabilisation via small order feedback controllers

The problem of stabilising a MIMO plant via output feedback controllers of a given degree was recently tackled via linearisation around some special degenerate compensators. This can be numerically implementated as an ε-perturbation method. The solution is in the form of a perturbation series which can be constructed by repetitively solving a set of linear equations, coming from the expansions (in ε and s) of the original pole placement equations. This expansion can be done almost trivially in any symbolic language using standard symbolic commands. The code is only a few lines long and can be done by the nonexpert. There is no need to understand the algebra of the problem, which involves tensor, polynomial algebra and some combinatorics since the load of the expansion is taken solely by the symbolic package