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On the Morgan problem with stability. (English) Zbl 0885.34055
The authors consider a linear, controllable, right invertible system of the form \[ \begin{cases} \dot x= Ax+Bu\\ y =Cx\end{cases} \] They are interested in the Morgan (decoupling) problem with stability. It consists in finding feedback laws \(u= Fx+Gv\) which put the transfer function into a diagonal form, while ensuring at the same time internal stability. For the solution of this problem, the authors give necessary and sufficient conditions. The method relies on the basic properties of the ring of proper and stable rational functions over \(\mathbb{R}\).

34H05 Control problems involving ordinary differential equations
93B27 Geometric methods
93B11 System structure simplification
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