Leverrier's algorithm and Cayley–Hamilton theorem for 2-D system

A Leverrier-like algorithm is presented which allows the computation of the transfer function of a linear regular system from its 2-D state-space description, without inverting a multivariable polynomial matrix. This algorithm is an extension of the classic Leverrier's algorithm for 1-D system and it reduces the computational cost. 2-D Cayley-Hamilton theorem is also shown by the algorithm.