An Explicit Method for Stability Analysis of 2D Systems Described by Transfer Function

In this paper, we propose a method to test the stability of two-dimensional (2D) linear discrete systems described by transfer function. And a complete region of disturbance parameters is solved to ensure the considered system with perturbations stability. Different from any other traditional algebraic methods, the algorithm of this method is explicit, which a large number of higher-order polynomial iterative operation doesn’t need to be carried out. By the fractional linear transformations, new condition is given in Hurwitz theorem, which doesn’t involve fractional calculation. The method is non-conservative for stability analysis and solving stable parameter region of 2D systems. It simplifies some existing methods. The computational cost is reduced. And it is better to solve the stability problems for 2D systems with disturbances. Examples illustrate the efficiency for testing the stability of higher-order 2D system and solving the robust stability problem of uncertain 2D systems.