On Jury´s test for 2-D stability of discrete-time systems and its simplification by telepolation

The paper revises and simplifies Jury´s tabular stability test for two-dimensional (2-D) discrete-time systems. The tabular test builds for a 2-D polynomial of degree (n₁, n₂) a `2-D table´-a sequence of n₂ matrices or equivalently 2-D polynomials and then examines its last entry-a 1-D polynomial of degree 2n₁n₂ for no zeros on the unit circle. Analysis of the cost of computation for the test is performed and shows that it is of O(n⁶) (n₁=n₂=n), compared to previous tabular tests of exponential complexity. Next, we propose a new test based on telepolation-telescoping the last entry of this 2-D table by interpolation. The table´s construction is replaced by n₁n ₂+1 stability tests of 1-D polynomials of degree n₁ or n₂. The resulting new 2-D stability test is shown to require a low O(n⁴) count of operations