IEEE/CAA Journal of Automatica Sinica
Citation:  Mohammad Hejri, "Global Practical Stabilization of DiscreteTime Switched Affine Systems via a General Quadratic Lyapunov Function and a Decentralized Ellipsoid," IEEE/CAA J. Autom. Sinica, vol. 8, no. 11, pp. 18371851, Nov. 2021. doi: 10.1109/JAS.2021.1004183 
[1] 
D. Liberzon, Switching in Systems and Control, T. Basar, Ed. Bikhauser Boston, 2003.

[2] 
G. S. Deaecto, J. C. Geromel, F. S. Garcia, and J. A. Pomilio, “Switched affine systems control design with application to DCDC converters,” IET Control Theory and Applications, vol. 4, no. 7, pp. 1201–1210, 2009.

[3] 
S. Baldi, A. Papachristodoulou, and E. B. Kosmatopoulos, “Adaptive pulse width modulation design for power converters based on affine switched systems,” Nonlinear Analysis:Hybrid Systems, vol. 30, pp. 306–322, 2018. doi: 10.1016/j.nahs.2018.07.002

[4] 
V. L. Yoshimora, E. Assuncao, E. R. P. da Silva, and M. C. M. Teixeira, “Observerbased control design for switched affine systems and applications to DCDC converters,” Journal of Control,Automation and Electrical Systems, vol. 24, no. 4, pp. 535–543, 2013. doi: 10.1007/s403130130044z

[5] 
T. Wang, Y. Liu, X. Wang, and J. Li, “Robust samplingbased switching design for piecewise affine systems with application to DCDC converters,” IET Control Theory &Applications, vol. 13, no. 9, pp. 1404–1412, 2019.

[6] 
C. Albea, G. Garcia, and L. Zaccarian, “Hybrid dynamic modeling and control of switched affine systems: Application to DCDC converters,” in Proc. IEEE 54th Annual Conf. Decision and Control, Osaka, Japan, Dec. 2015, pp. 2264–2269.

[7] 
G. Beneux, P. Riedinger, J. Daafouz, and L. Grimaud, “Adaptive stabilization of switched affine systems with unknown equilibrium points: Application to power converters,” Automatica, vol. 99, pp. 82–91, 2019. doi: 10.1016/j.automatica.2018.10.015

[8] 
M. Hejri, A. Giua, and H. Mokhtari, “On the complexity and dynamical properties of mixed logical dynamical systems via an automatonbased realization of discretetime hybrid automaton,” Int. Journal of Robust and Nonlinear Control, vol. 28, no. 16, pp. 4713–4746, 2018. doi: 10.1002/rnc.4278

[9] 
G. S. Deaecto and J. C. Geromel, “Stability analysis and control design of discretetime switched affine systems,” IEEE Trans. Automatic Control, vol. 62, no. 8, pp. 4058–4065, Aug. 2017. doi: 10.1109/TAC.2016.2616722

[10] 
L. N. Egidio and G. S. Deaecto, “Novel practical stability conditions for discretetime switched affine systems,” IEEE Trans. Automatic Control, vol. 64, no. 11, pp. 4705–4710, 2019. doi: 10.1109/TAC.2019.2904136

[11] 
C. Albea Sanchez, G. Garcia, H. Sabrina, W. P. M. H. Heemels, and L. Zaccarian, “Practical stabilisation of switched affine systems with dwelltime guarantees,” IEEE Trans. Automatic Control, vol. 64, no. 11, pp. 4811–4817, 2019. doi: 10.1109/TAC.2019.2907381

[12] 
Z. Li, D. Ma, and J. Zhao, “Dynamic eventtriggered L_{∞} control for switched affine systems with sampleddata switching,” Nonlinear Analysis:Hybrid Systems, vol. 39, pp. 1–12, 2021.

[13] 
S. Ding, X. Xie, and Y. Liu, “Eventtriggered static/dynamic feedback control for discretetime linear systems,” Information Sciences, vol. 524, 2020.

[14] 
S. Ding and Z. Wang, “Eventtriggered synchronization of discretetime neural networks: A switching approach,” Neural Networks, vol. 125, 2020.

[15] 
X. Xu and G. Zhai, “Practical stability and stabilization of hybrid and switched systems,” IEEE Trans. Automatic Control, vol. 50, no. 11, pp. 1897–1903, Nov. 2005. doi: 10.1109/TAC.2005.858680

[16] 
X. Xu, G. Zhai, and S. He, “On practical asymptotic stabilizability of switched affine systems,” Nonlinear Analysis:Hybrid Systems, vol. 2, no. 1, pp. 196–208, 2008. doi: 10.1016/j.nahs.2007.07.003

[17] 
X. Xu, G. Zhai, and S. He, “Some results on practical stabilizability of discretetime switched affine systems,” Nonlinear Analysis: Hybrid Systems, vol. 4, no. 1, pp. 113–121, 2010.

[18] 
V. Lakshmikantham, S. Leela, and A. A. Martynyuk, Practical Stability of Nonlinear Systems. World Scientific, 1990.

[19] 
A. Loría and E. Panteley, Stability, Told by Its Developers. London: Springer London, 2006, pp. 199–258.

[20] 
M. Hejri, “Global practical stabilization of discretetime switched affine systems via switched lyapunov functions and statedependent switching functions,” Scientia Iranica, Transaction D, Computer Science & Electrical Engineering, DOI: 10.24200/SCI.2020.54524.3793, 2020.

[21] 
M. Hejri, “On the global practical stabilization of discretetime switched affine systems: Application to switching power converters,” Scientia Iranica, Transaction D, Computer Science & Electrical Engineering, DOI: 10.24200/SCI.2020.55427.4217, 2020.

[22] 
L. Hetel and E. Fridman, “Robust sampleddata control of switched affine systems,” IEEE Trans. Automatic Control, vol. 58, no. 11, pp. 2922–2928, Nov. 2013. doi: 10.1109/TAC.2013.2258786

[23] 
G. S. Deaecto and L. N. Egidio, “Practical stability of discretetime switched affine systems,” in Proc. European Control Conf., Aalborg, Denmark, 2016, pp. 2048–2053.

[24] 
C. A. Sanchez, A. VentosaCutillas, A. S. A, and F. Gordillo, “Robust switching control design for uncertain discretetime switched affine systems,” Int. Journal of Robust and Nonlinear Control, vol. 30, no. 17, pp. 7089–7102, 2020. doi: 10.1002/rnc.5158

[25] 
P. Bolzern and W. Spinelli, “Quadratic stabilization of a switched affine system about a nonequilibrium point,” in Proc. American Control Conf. Boston, Massachusetts: IEEE, June 30–July 2 2004, pp. 3890–3895.

[26] 
G. S. Deaecto and G. C. Santos, “State feedback H_{∞} control design of continuoustime switchedaffine systems,” IET Control Theory and Applications, vol. 9, no. 10, pp. 1511–1516, 2014.

[27] 
G. S. Deaecto, “Dynamic output feedback H_{∞} control of continuoustime switched affine systems,” Automatica, vol. 71, pp. 44–49, 2016. doi: 10.1016/j.automatica.2016.04.022

[28] 
A. Poznyak, A. Polyakov, and V. Azhmyakov, Attractive Ellipsoids in Robust Control, T. Basar, Ed. Birkhauser, 2014.

[29] 
C. Perez, V. Azhmyakov, and A. Poznyak, “Practical stabilization of a class of switched systems: Dwelltime approach,” IMA Journal of Mathematical Control and Information, vol. 32, no. 4, pp. 689–702, May 2014.

[30] 
H. Khalil, Nonlinear Systems, 3rd ed. Prentice Hall, 2003.

[31] 
S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory. Society for Industrial and Applied Mathematics, SIAM, 1994.

[32] 
J. Lofberg, “YALMIP: A toolbox for modeling and optimization in MATLAB,” in Proc. IEEE Int. Symp. Computer Aided Control Systems Design, Taipei, China, Sept. 2004, pp. 284–289.

[33] 
G.R. Duan and H.H. Yu, LMIs in Control Systems: Analysis, Design and Applications. CRC Press, Taylor & Francis Group, 2013.

[34] 
M. Kocvara and M. Stingl, PENBMI Users Guide (Version 2.1), www.penopt.com, March 5 2006.

[35] 
M. J. Lacerda and T. da Silveira Gomide, “Stability and stabilizability of switched discretetime systems based on structured Lyapunov functions,” IET Control Theory &Applications, vol. 14, no. 5, pp. 781–789, 2020.

[36] 
A. Hassibi, J. How, and S. Boyd, “A pathfollowing method for solving bmi problems in control,” in Proc. American Control Conf., San Diego, California, 1999, pp. 1385–1389.

[37] 
W.Y. Chiu, “Method of reduction of variables for bilinear matrix inequality problems in system and control designs,” IEEE Trans. Systems,Man,and Cybernetics:Systems, vol. 47, no. 7, pp. 1241–1256, Jul. 2017. doi: 10.1109/TSMC.2016.2571323

[38] 
M. Hejri and A. Giua, “Hybrid modeling and control of switching DCDC converters via MLD systems,” in Proc. IEEE 7th Int. Conf. Automation Science and Engineering, Trieste, Italy, Aug. 2011, pp. 714–719.
