Improved neural network for checking the stability of multidimensional systems

In this paper, the author´s previous work is extended and a new neural network is utilized to solve the stability problem of multidimensional systems. In the original authors work the problem is transformed into an optimization problem. Using the DeCarlo-Strintzis Theorem one has to check if |B(Z₁,..., 1, Z_m)| ≠ 0 for |Z₁| = ... = |Z_m| = 1 or equivalently if the min |B(Z₁, ..., 1, Z_m)| is 0 or not, where B(Z₁, Z₂, ..., Z_m) is the denominator of the discrete transfer funcion. Then, the problem is reduced to a minimization problem and a neural network is proposed for solving it. To improve the chance of convergence towards the global minimum, an extension of this neural network based on random noise terms is proposed in this contribution. The numerical examples illustrate the validity and the efficiency of the new neural network.