Relative Controllability for Delayed Linear Discrete System with Second-Order Differences

• Maosong Yang ^[3] ; Michal Feˇckan ^[1] ; JinRong Wang ^[2]
  1. [1] Comenius University

     Comenius University

     Eslovaquia

     
  2. [2] Guizhou University

     Guizhou University

     China

     
  3. [3] Guizhou University & Guizhou Open University

  Mostrar afiliaciones +
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • In this work, with the aid of the representation of the solution, the relative controllability for delaying linear discrete systems with a second-order difference is principally investigated. Utilizing the delayed discrete matrix function, we give a sufficient criteria for relative controllability, and construct a relevant control function. Lastly, an example is presented to demonstrate the effectiveness of theoretical result.

• Referencias bibliográficas
  • 1. Elaydi, S.: An Introduction to Difference Equations, 3rd edn. Springer, New York (2005)
  • 2. Klamka, J.: Controllability of linear systems with time-variable delays in control. Int. J. of Control 24, 869–878 (1976)
  • 3. Klamka, J.: Relative controllability of nonlinear systems with delays in control. Autom. 12, 633–634 (1976)
  • 4. Klamka, J.: On the controllability of linear systems with delays in the control. Int. J. of Control 25, 875–883 (1977)
  • 5. Khusainov, D.Y., Shuklin, G.V.: Relative controllability in systems with pure delay. Int. Appl. Mech. 41, 210–221 (2005)
  • 6. Balachandran, K., Kokila, J., Trujillo, J.J.: Relative controllability of fractional dynamical systems with multiple delays in control....
  • 7. Liang, C., Wang, J., O’Regan, D.: Controllability of nonlinear delay oscillating systems. Electron. J. of Qual. Theory of Differential...
  • 8. Li, M., Debbouche, A., Wang, J.: Relative controllability in fractional differential equations with pure delay. Math. Methods in the Appl....
  • 9. Wang, X., Wang, J., Feˇckan, M.: Controllability of conformable differential systems. Nonlinear Anal.: Modelling and Control 25, 658–674...
  • 10. You, Z., Feˇckan, M., Wang, J.: Relative controllability of fractional delay differential equations via delayed perturbation of Mittag-Leffler...
  • 11. You, Z., Feˇckan, M., Wang, J.: On the relative controllability of neutral delay differential equations. J. of Math. Phys. 62, 082704...
  • 12. Wang, J., Sathiyaraj, T., O’Regan, D.: Relative controllability of a stochastic system using fractional delayed sine and cosine matrices....
  • 13. Shukla, A., Patel, R.: Controllability results for fractional semilinear delay control systems. J. of Appl. Math. and Comput. 65, 861–875...
  • 14. You, Z., Feˇckan, M., Wang, J., O’Regan, D.: Relative controllability of impulsive multi-delay differential systems. Nonlinear Anal.:...
  • 15. Diblík, J., Khusainov, D.Y., R ˚užiˇcková, M.: Controllability of linear discrete systems with constant coefficients and pure delay. SIAM...
  • 16. Diblík, J., Fe´ckan, M., Pospí´sil, M.: On the new control functions for linear discrete delay systems. SIAM J. on Control and Optim....
  • 17. Pospíšil, M., Diblík, J., Feˇckan, M.: On relative controllability of delayed difference equations with multiple control functions. AIP...
  • 18. Mazanti, G.: Relative controllability of linear difference equations. SIAM J. on Control and Optim. 55, 3132–3153 (2017)
  • 19. Pospíšil, M.: Relative controllability of delayed difference equations to multiple consecutive states. AIP Conf. Proc. 2017, 480002–1–480002–4...
  • 20. Diblík, J.: Relative and trajectory controllability of linear discrete systems with constant coefficients and a single delay. IEEE Trans....
  • 21. Diblík, J., Mencáková, K.: A note on relative controllability of higher order linear delayed discrete systems. IEEE Trans. on Autom. Control...
  • 22. Mencáková, K., Diblík, J.: Relative controllability of a linear system of discrete equations with single delay. AIP Conf. Proc. 2293,...
  • 23. Khusainov, D.. Ya.., Shuklin, G.V.: Linear autonomous time-delay system with permutation matrices solving. Stud. Univ. Žilina 17, 101–108...
  • 24. Diblík, J., Khusainov, D.Y.: Representation of solutions of discrete delayed system x(k+1) = Ax(k)+ Bx(k − m) + f (k)...
  • 25. Diblík, J., Khusainov, D.Y.: Representation of solutions of linear discrete systems with constant coefficients and pure delay. Adv. in...
  • 26. Diblík, J., Morávková, B.: Representation of the solutions of linear discrete systems with constant coefficients and two delays. Abstract...
  • 27. Diblík, J., Mencáková, K.: Representation of solutions to delayed linear discrete systems with constant coefficients and with second-order...
  • 28. Diblík, J., Halfarová, H.: Explicit general solution of planar linear discrete systems with constant coefficients and weak delays. Adv....
  • 29. Pospíšil, M.: Representation of solutions of delayed difference equations with linear parts given by pairwise permutable matrices via...
  • 30. Diblík, J.: Exponential stability of linear discrete systems with nonconstant matrices and nonconstant delay. AIP Conf. Proc. 2017, 480003-1-480003–4...
  • 31. Diblík, J., Khusainov, D.Y., R ˚užiˇcková, M.: Exponential stability of linear discrete systems with delay. AIP Conf. Proc. 2018, 430004-1-430004–4...
  • 32. Baštinec, J., Diblík, J., Khusainov, D.: Stability of linear discrete systems with variable delays. AIP Conf. Proc. 2018, 430005-1-430005-4...
  • 33. Khusainov, D.Y., Shuklin, G.V.: Relative controllability in systems with pure delay. Int. Appl. Mech. 41, 210–221 (2005)
  • 34. Liang, C., Wang, J., Feˇckan, M.: A study on ILC for linear discrete systems with single delay. J. of Difference Equations and Appl. 24,...
  • 35. Liang, C., Wang, J., Shen, D.: Iterative learning control for linear discrete delay systems via discrete matrix delayed exponential function...
  • 36. Jin, X., Wang, J., Shen, D.: Convergence analysis for iterative learning control of impulsive linear discrete delay systems. J. of Difference...
  • 37. Jin, X., Wang, J.: Iterative learning control for linear discrete delayed systems with non-permutable matrices. Bulletin of the Iranian...