Open Access

Quadratic Performance Analysis of Switched Affine Time–Varying Systems


Cite

Allerhand, L.I. and Shaked, U. (2011). Robust stability and stabilization of linear switched systems with dwell time, IEEE Transactions on Automatic Control 56(2): 381-386.10.1109/TAC.2010.2097351Search in Google Scholar

Bolzern, P. and Spinelli, W. (2004). Quadratic stabilization of as witched affine system about a nonequilibrium point, Proceedings of the American Control Conference, Boston, MA, USA, pp. 3890-3895.10.23919/ACC.2004.1383918Search in Google Scholar

Branicky, M.S. (1998). Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Transactions on Automatic Control 43(4): 475-482.10.1109/9.664150Search in Google Scholar

Deaecto, G.S. (2016). Dynamic output feedback H∞ control of continuous-time switched affine systems, Automatica 71(1): 44-49.10.1016/j.automatica.2016.04.022Search in Google Scholar

Deaecto, G.S. and Santos, G.C. (2015). State feedback H∞ control design of continuous-time switched affine systems, IET Control Theory & Applications 9(10): 1511-1516.10.1049/iet-cta.2014.0153Search in Google Scholar

DeCarlo, R., Branicky, M.S., Pettersson, S. and Lennartson, B. (2000). Perspectives and results on the stability and stabilizability of hybrid systems, Proceedings of the IEEE 88(7): 1069-1082.10.1109/5.871309Search in Google Scholar

Feron, E. (1996). Quadratic stability of switched systems via state and output feedback, MIT Technical Reports CICSP- 468, MIT, Cambridge, MA.Search in Google Scholar

Hetel, L. and Fridman, E. (2013). Robust sampled-data control of switched affine systems, IEEE Transactions on Automatic Control 58(11): 2922-2928.10.1109/TAC.2013.2258786Search in Google Scholar

Leth, J. and Wisniewski, R. (2014). Local analysis of hybrid systems on polyhedral sets with state-dependent switching, International Journal of Applied Mathematics and Computer Science 24(2): 341-355, DOI: 10.2478/amcs-2014-0026.10.2478/amcs-2014-0026Open DOISearch in Google Scholar

Liberzon, D. (2003). Switching in Systems and Control, Birkh¨auser, Boston, MA.10.1007/978-1-4612-0017-8Search in Google Scholar

Liberzon, D. andMorse, A.S. (1999). Basic problems in stability and design of switched systems, IEEE Control Systems Magazine 19(5): 59-70.10.1109/37.793443Search in Google Scholar

Luis-Delgado, J.D., Al-Hadithi, B.M. and Jim´enez, A. (2017). A novel method for the design of switching surfaces for discretized MIMO nonlinear systems, International Journal of Applied Mathematics and Computer Science 27(1): 5-17, DOI: 10.1515/amcs-2017-0001.10.1515/amcs-2017-0001Open DOISearch in Google Scholar

Packard, A. (1994). Gain scheduling via linear fractional transformation, Systems & Control Letters 22(2): 79-92.10.1016/0167-6911(94)90102-3Search in Google Scholar

Pettersson, S. and Lennartson, B. (2002). Hybrid system stability and robustness verification using linear matrix-inequalities, International Journal of Control 75(16-17): 1335-1355.10.1080/0020717021000023762Search in Google Scholar

Scharlau, C.C., de Oliveira, M.C., Trofino, A. and Dezuo, T.J.M. (2014). Switching rule design for affine switched systems using a max-type composition rule, Systems & Control Letters 68(1): 1-8.10.1016/j.sysconle.2014.02.007Search in Google Scholar

Skelton, R.E., Iwasaki, T. and Grigoriadis, K.M. (1998). A Unified Algebraic Approach to Linear Control Design, Taylor & Francis, London.Search in Google Scholar

Sun, Z. and Ge, S.S. (2005). Switched Linear Systems: Control and Design, Springer, London.10.1007/1-84628-131-8Search in Google Scholar

Trofino, A., Assmann, D., Scharlau, C.C. and Coutinho, D.F. (2009). Switching rule design for switched dynamic systems with affine vector fields, IEEE Transactions on Automatic Control 54(9): 2215-2222.10.1109/TAC.2009.2026848Search in Google Scholar

van der Schaft, A. and Schumacher, H. (2000). An Introduction to Hybrid Dynamical Systems, Springer, London.10.1007/BFb0109998Search in Google Scholar

Wicks, M.A., Peleties, P. and DeCarlo, R. A. (1998). Switched controller design for the quadratic stabilization of a pair of unstable linear systems, European Journal of Control 4(2): 140-147.10.1016/S0947-3580(98)70108-6Search in Google Scholar

Xiang, W. (2016). Necessary and sufficient condition for stability of switched uncertain linear systems under dwell-time constraint, IEEE Transactions on Automatic Control 61(11): 3619-3624.10.1109/TAC.2016.2524996Search in Google Scholar

Xiang, W. and Xiao, J. (2014). Stabilization of switched continuous-time systems with all modes unstable via dwell time switching, Automatica 50(3): 940-945.10.1016/j.automatica.2013.12.028Search in Google Scholar

Xiang, Z., Wang, R. and Chen, Q. (2010). Fault tolerant control of switched nonlinear systems with time delay under asynchronous switching, International Journal of Applied Mathematics and Computer Science 20(3): 497-506, DOI: 10.2478/v10006-010-0036-0.10.2478/v10006-010-0036-0Open DOISearch in Google Scholar

Xu, X. and Zhai, G. (2005). Practical stability and stabilization of hybrid and switched systems, IEEE Transactions on Automatic Control 50(11): 1897-1903.10.1109/TAC.2005.858680Search in Google Scholar

Xu, X., Zhai, G. and He, S. (2008). On practical asymptotic stabilizability of switched affine systems, Nonlinear Analysis: Hybrid Systems 2(1): 196-208.10.1016/j.nahs.2007.07.003Search in Google Scholar

Yoshimura, V.L., Assuncao, E., da Silva, E.R.P., Teixeira, M.C.M. and Mainardi Jr., E.I. (2013). Observer-based control design for switched affine systems and applications to DC-DC converters, Journal of Control, Automation and Electrical Systems 24(4): 535-543.10.1007/s40313-013-0044-zSearch in Google Scholar

Zhai, G. (2001). Quadratic stabilizability of discrete-time switched systems via state and output feedback, Proceedings of the Conference on Decision and Control, Orlando, Florida, FL, USA, pp. 2165-2166.Search in Google Scholar

Zhai, G. (2012). Quadratic stabilizability and H∞ disturbance attenuation of switched linear systems via state and output feedback, Proceedings of the Conference on Decision and Control, Maui, HI, USA, pp. 1935-1940.Search in Google Scholar

Zhai, G. (2015). A generalization of the graph Laplacian with application to a distributed consensus algorithm, International Journal of Applied Mathematics and Computer Science 25(2): 353-360, DOI: 10.1515/amcs-2015-0027.10.1515/amcs-2015-0027Open DOISearch in Google Scholar

Zhai, G., Hu, B., Yasuda, K. and Michel, A.N. (2001). Disturbance attenuation properties of time-controlled switched systems, Journal of The Franklin Institute 338(7): 765-779.10.1016/S0016-0032(01)00030-8Search in Google Scholar

Zhai, G. and Huang, C. (2015). A note on basic consensus problems in multi-agent systems with switching interconnection graphs, International Journal of Control 88(3): 631-639.10.1080/00207179.2014.971431Search in Google Scholar

Zhai, G., Lin, H. and Antsaklis, P.J. (2003). Quadratic stabilizability of switched linear systems with polytopic uncertainties, International Journal of Control 76(7): 747-753.10.1080/0020717031000114968Search in Google Scholar

Zhai, G., Xu, X., Lin, H. and Liu, D. (2007). Extended Lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems, International Journal of Applied Mathematics and Computer Science 17(4): 447-454, DOI: 10.2478/v100006-007-0036-x.10.2478/v100006-007-0036-xOpen DOISearch in Google Scholar

eISSN:
2083-8492
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics