论文信息 - The Schur stability via the Hurwitz stability analysis using a biquadratic transformation

The Schur stability via the Hurwitz stability analysis using a biquadratic transformation

In this note, it is shown that instead of a bilinear transformation, a biquadratic transformation can be used to determine the Schur stability of a given discrete-time polynomial by determining the Hurwitz stability of the corresponding continuous-time polynomial. However, using a biquadratic transformation, the analysis is not limited by any restriction on the root positions. Several numerical examples are provided to illustrate the procedure.

Babak Nadjar Araabi | Mahdi Jalili

[1] H. Power. Application of bilinear transformation to root locus plotting , 1970 .

[2] Kishan Shenoi. Digital Signal Processing In Telecommunications , 1995 .

[3] H. Inaba,et al. The property of bilinear transformation matrix and Schur stability for a linear combination of polynomials , 1999 .

[4] Shankar P. Bhattacharyya,et al. Plant-robust and controller-robust discrete-time PID design , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[5] Benjamin C. Kuo,et al. Digital Control Systems , 1977 .

[6] Mohammad Aldeen,et al. Bilinear transformation and generalized singular perturbation model reduction , 1996, IEEE Trans. Autom. Control..

[7] L. Volfson,et al. S-plane to Z-plane mapping using a simultaneous equation algorithm based on the bilinear transformation , 1987 .

[8] Shankar P. Bhattacharyya,et al. Computation of all stabilizing PID gains for digital control systems , 2001, IEEE Trans. Autom. Control..

[9] Katsuhiko Ogata,et al. Discrete-time control systems , 1987 .