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 33 articles )

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  1. Zhan, Xuzhou; Dyachenko, Alexander: On generalization of classical Hurwitz stability criteria for matrix polynomials (2021)
  2. Dzhafarov, Vakif; Esen, Özlem; Büyükköroğlu, Taner: On polytopes in Hurwitz region (2020)
  3. Dzhafarov, Vakif; Esen, Özlem; Büyükköroğlu, Taner: Infinite polytopes in Hurwitz stability region (2019)
  4. Berman, Abraham (ed.); Bomze, Immanuel M. (ed.); Dür, Mirjam (ed.); Shaked-Monderer, Naomi (ed.): Copositivity and complete positivity. Abstracts from the workshop held October 29 -- Novermber 4, 2017 (2017)
  5. Boito, P.; Eidelman, Y.; Gemignani, L.: Implicit QR for companion-like pencils (2016)
  6. Heß, Roxana; Henrion, Didier; Lasserre, Jean-Bernard; Phạm, Tien Son: Semidefinite approximations of the polynomial abscissa (2016)
  7. Lasserre, Jean B.: A generalization of Löwner-John’s ellipsoid theorem (2015)
  8. Ou, Liuli; Han, Shaobo; Wang, Yongji; Dong, Shuai; Liu, Lei: Partial pole placement in LMI region (2014)
  9. Zhao, Yan; Zhang, Tieyan; Zhao, Dan; You, Fucai; Li, Miao: Robust stability criteria of Roesser-type discrete-time two-dimensional systems with parameter uncertainties (2014)
  10. Niamsup, P.; Rajchakit, G.: New results on robust stability and stabilization of linear discrete-time stochastic systems with convex polytopic uncertainties (2013)
  11. Yang, Li; Yu, Bo: A homotopy method for nonlinear semidefinite programming (2013)
  12. Efimov, Denis; Fridman, Leonid; Raïssi, Tarek; Zolghadri, Ali; Seydou, Ramatou: Interval estimation for LPV systems applying high order sliding mode techniques (2012)
  13. Henrion, Didier; Vyhlídal, Tomáš: Positive trigonometric polynomials for strong stability of difference equations (2012)
  14. Rajchakit, M.; Rajchakit, G.: LMI approach to robust stability and stabilization of nonlinear uncertain discrete-time systems with convex polytopic uncertainties (2012)
  15. Lee, Dong Hwan; Park, Jin Bae; Joo, Young Hoon: A less conservative LMI condition for robust (\mathcalD)-stability of polynomial matrix polytopes -- a projection approach (2011)
  16. Mao, Wei-Jie: An LMI approach to (\mathcalD)-stability and (\mathcalD)-stabilization of linear discrete singular systems with state delay (2011)
  17. Delibaşı, Akın; Henrion, Didier: Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities (2010)
  18. Minh, Vu Trieu; Hashim, Fakhruldin Bin Mohd: Robust model predictive control schemes for tracking setpoints (2010)
  19. Phat, Vu N.; Nam, Phan T.: Exponential stability of delayed Hopfield neural networks with various activation functions and polytopic uncertainties (2010)
  20. Franzè, Giuseppe; Casavola, Alessandro; Famularo, Domenico; Garone, Emanuele: An off-line MPC strategy for nonlinear systems based on SOS programming (2009)

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