Controllability, pole placement, and stabilizability for homogenous polynomial systems

In linear system theory the concepts of controllability, pole assignment, and stabilizability are very familiar. These topics are now addressed for the class of homogeneous polynomial systems. First, general results on necessary conditions for the state controllability are derived using results from linear algebra and algebraic geometry. Then pole placement and stabilizability results are developed for the two-dimensional case. Finally, practical examples illustrate the results.