Stability of multidimensional systems using genetic algorithms

The study of the stability of m-dimensional systems is a difficult one especially when m ≥ 3. There exist only a few results in the literature and unfortunately, there does not exist any practical criterion. In this work, the stability of an m-dimensional system is dealt as a minimization problem of the absolute value of its characteristic polynomial over the boundaries of its variables (i.e., on the m unit circles). This minimization problem is solved by using genetic algorithms (GAs). Using GAs we obtain, in general, better results than other methods of minimization (numerical techniques, neural networks, etc.). Numerical examples are presented.