Further Improvements on Bose's 2D Stability Test

This paper proposes some further improvements on N.K. Bose's 2D stability test for polynomials with real coefficients by revealing symmetric properties of the polynomials, resultants occurring in the test and by generalizing Sturm's method. The improved test can be fulfilled by a totally algebraic algorithm with a finite number of steps and the computational complexity is largely reduced as it involves only certain real variable polynomials with degrees not exceeding half of their previous complex variable counterparts. Nontrivial examples for 2D polynomials having both numerical and literal coefficients are also shown to illustrate the computational advantage of the proposed method.