Polynomial Toolbox

Discrete-time symmetric polynomial equations with complex coefficients. Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial Toolbox for Matlab.

References in zbMATH (referenced in 28 articles )

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  1. Boito, P.; Eidelman, Y.; Gemignani, L.: Implicit QR for companion-like pencils (2016)
  2. Heß, Roxana; Henrion, Didier; Lasserre, Jean-Bernard; Phạm, Tien Son: Semidefinite approximations of the polynomial abscissa (2016)
  3. Lasserre, Jean B.: A generalization of Löwner-John’s ellipsoid theorem (2015)
  4. Ou, Liuli; Han, Shaobo; Wang, Yongji; Dong, Shuai; Liu, Lei: Partial pole placement in LMI region (2014)
  5. Niamsup, P.; Rajchakit, G.: New results on robust stability and stabilization of linear discrete-time stochastic systems with convex polytopic uncertainties (2013)
  6. Yang, Li; Yu, Bo: A homotopy method for nonlinear semidefinite programming (2013)
  7. Efimov, Denis; Fridman, Leonid; Raïssi, Tarek; Zolghadri, Ali; Seydou, Ramatou: Interval estimation for LPV systems applying high order sliding mode techniques (2012)
  8. Henrion, Didier; Vyhlídal, Tomáš: Positive trigonometric polynomials for strong stability of difference equations (2012)
  9. Rajchakit, M.; Rajchakit, G.: LMI approach to robust stability and stabilization of nonlinear uncertain discrete-time systems with convex polytopic uncertainties (2012)
  10. Lee, Dong Hwan; Park, Jin Bae; Joo, Young Hoon: A less conservative LMI condition for robust $\cal D$-stability of polynomial matrix polytopes -- a projection approach (2011)
  11. Mao, Wei-Jie: An LMI approach to $\cal D$-stability and $\cal D$-stabilization of linear discrete singular systems with state delay (2011)
  12. Delibaşı, Akın; Henrion, Didier: Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities (2010)
  13. Minh, Vu Trieu; Hashim, Fakhruldin Bin Mohd: Robust model predictive control schemes for tracking setpoints (2010)
  14. Phat, Vu N.; Nam, Phan T.: Exponential stability of delayed Hopfield neural networks with various activation functions and polytopic uncertainties (2010)
  15. Franzè, Giuseppe; Casavola, Alessandro; Famularo, Domenico; Garone, Emanuele: An off-line MPC strategy for nonlinear systems based on SOS programming (2009)
  16. Zattoni, Elena: $H_2$-optimal rejection with preview: geometric constraints and dynamic feedforward solutions via spectral factorization (2008)
  17. Ahn, Hyo-Sung; Moore, Kevin L.; Chen, YangQuan: Iterative learning control. Robustness and monotonic convergence for interval systems. (2007)
  18. Li, Haibin; Wang, Zhizhen; Wang, Long; Li, Zhaoping; Li, Erxiao: Frequency domain criteria for robust $\cal D$-stability of MIMO systems based on LMI method (2006)
  19. Nurges, Ülo: Robust pole assignment via reflection coefficients of polynomials (2006)
  20. Boston, Nigel: Pipelined IIR filter architecture using pole-radius minimization (2005)

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