Algebraic stability criteria and symbolic derivation of stability conditions for feedback control systems

作者：Wang Dongming^*

来源：International Journal of Control, 2012, 85(10): 1414-1421.

DOI：10.1080/00207179.2012.686633

• feedback control
• stability condition
• Nyquist criterion
• Popov criterion
• circle criterion
• algebraic method
• symbolic computation

This article provides algebraic settings of the stability criteria of Nyquist and Popov and the circle criterion for closed-loop linear control systems with linear or nonlinear feedback whose transfer functions are rational ones with integer coefficients. The proposed settings make use of algebraic methods of parametric curve implicitisation, real root isolation, symbolic integration and quantifier elimination and allow one to derive exact stability conditions for feedback control systems with symbolic computation. An example is presented to illustrate the algebraic approach and its effectiveness. Some numerical stability results obtained previously are confirmed.

• 出版日期2012