Stability analysis of discrete-time switched systems: a switched homogeneous Lyapunov function method

References

• Allerhand, L.I., & Shaked, U. (2013). Robust estimation of linear switched systems with dwell time. International Journal of Control, 86(11), 2067–2074.
   Web of Science ®Google Scholar
• Blanchini, F., & Colaneri, P. (2010). Vertex/plane characterization of the dwell-time property for switching linear systems. In Alessandro Astolfi et al. (Eds.), Proceedings of the 49th IEEE Conference on Decision & Control (pp. 3258–3263). Atlanta, GA: IEEE.
   Google Scholar
• Blanchini, F., & Miani, S. (1999). A new class of universal Lyapunov functions for the control of uncertain linear systems. IEEE Transactions on Automatic Control, 44(3), 641–647.
   Web of Science ®Google Scholar
• Blanchini, F., & Miani, S. (2003). Stabilization of LPV systems: State feedback, state estimation, and duality. SIAM Journal on Control & Optimization, 42(1), 76–97.
   Web of Science ®Google Scholar
• Blanchini, F., & Miani, S. (2008). Set theoretic methods in control. Boston, MA: Birkhäuser.
   Google Scholar
• Brewer, J.W. (1978). Kronecker products and matrix calculus in system theory. IEEE Transactions on Circuits & Systems, 25(9), 772–781.
   Google Scholar
• Chesi, G., Colaneri, P., Geromel, J.C., Middleton, R., & Shorten, R. (2012). A nonconservative LMI condition for stability of switched systems with guaranteed dwell time. IEEE Transactions on Automatic Control, 57(5), 1297–1302.
   Web of Science ®Google Scholar
• Chesi, G., Garulli, A., Tesi, A., & Vicino, A. (2009). Homogeneous polynomial forms for robustness analysis of uncertain systems. New York, NY: Springer.
   Google Scholar
• Daafouz, J., Riedinger, P., & Iung, C. (2002). Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach. IEEE Transactions on Automatic Control, 47(11), 1883–1887.
   Web of Science ®Google Scholar
• Dayawansa, W.P., & Martin, C.F. (1999). A converse Lyapunov theorem for a class of dynamical systems which undergo switching. IEEE Transactions on Automatic Control, 44(4), 751–760.
   Web of Science ®Google Scholar
• Deaecto, G.S., Fioravanti, A.R., & Geromel, J.C. (2013). Suboptimal switching control consistency analysis for discrete-time switched linear systems. European Journal of Control, 19(3), 214–219.
   Web of Science ®Google Scholar
• Dehghan, M., & Ong, C.-J. (2012). Discrete-time switching linear system with constraints: Characterization and computation of invariant sets under dwell-time consideration. Automatica, 48(5), 964–969.
   Web of Science ®Google Scholar
• Geromel, J.C., & Colaneri, P. (2006). Stability and stabilization of discrete time switched systems. International Journal of Control, 79(7), 719–728.
   Web of Science ®Google Scholar
• Goebel, R., Sanfelice, R.G., & Teel, A.R. (2009). Hybrid dynamical systems. IEEE Control Systems Magazine, 29(2), 28–93.
   Web of Science ®Google Scholar
• Liberzon, D. (2003). Switching in systems and control. Boston: Springer Verlag.
   Google Scholar
• Liu, X. (2009). Stability analysis of switched positive systems: A switched linear copositive Lyapunov function method. IEEE Transactions on Circuits & Systems II: Express Briefs, 56(5), 414–418.
   Web of Science ®Google Scholar
• Liu, X., & Liu, D. (2014). Equivalence between different stabilities of discrete-time delayed switched systems with uncertainties. In Alessandro Astolfi et al. (Eds.), Proceedings on the 53rd IEEE Conference on Decision & Control (pp. 5457–5462). Los Angeles, CA: IEEE.
   Google Scholar
• Sun, Z., & Ge, S.S. (2011). Stability theory of switched dynamical systems. London: Springer-Verlag.
   Google Scholar
• Sun, Y., & Wang, L. (2013). On stability of a class of switched nonlinear systems. Automatica, 49(1), 305–307.
   Web of Science ®Google Scholar
• Yang, Y., Xiang, C., & Lee, T.H. (2012). Sufficient and necessary conditions for the stability of second-order switched linear systems under arbitrary switching. International Journal of Control, 85(12), 1977–1995.
   Web of Science ®Google Scholar
• Zhang, L., Cui, N., Liu, M., & Zhao, Y. (2011). Asynchronous filtering of discrete-time switched linear systems with average dwell time. IEEE Transactions on Circuits & Systems I: Regular Papers, 58(5), 1109–1118.
   Web of Science ®Google Scholar
• Zhang, W., Abate, A., Hu, J., & Vitus, M.P. (2009). Exponential stabilization of discrete-time switched linear systems. Automatica, 45(11), 2526–2536.
   Web of Science ®Google Scholar
• Zhao, X., Liu, X., Yin, S., & Li, H. (2014). Improved results on stability of continuous-time switched positive linear systems. Automatica, 50(2), 614–621.
   Web of Science ®Google Scholar