References
- Alpin, Y., Elsner, L., & Ikramov, K. (2000). On condensed forms for partially commuting matrices. Linear Algebra and its Applications, 306(1–3), 165–182.
- Beker, O., Hollot, C., Chait, Y., & Han, H. (2004). Fundamental properties of reset control systems. Automatica, 40(6), 905–915.
- Brás, I., Carapito, A.C., & Rocha, P. (2006). Stability of interconnected switched systems. In Proceedings of the 7th Portuguese Conference on Automatic Control (pp. 1–6). Associação Portuguesa de Controlo Automático, Lisbon, Portugal.
- Brás, I., Carapito, A.C., & Rocha, P. (2013). Stability of switched systems with partial state reset. IEEE Transactions on Automatic Control, 58(4), 1008–1012.
- Cheng, D., Guo, L., & Huang, J. (2003). On quadratic Lyapunov functions. IEEE Transactions on Automatic Control, 48, 885–890.
- Hespanha, J.P., & Morse, A.S. (2002). Switching between stabilizing controllers. Automatica, 38, 1905–1917.
- Hespanha, J.P., Santesso, P., & Stewart, G. (2007). Optimal controller initialization for switching between stabilizing controllers. In Proceeding of the 46th IEEE Conference on Decision and Control (pp. 5511–5516). IEEE, New Orleans, LA.
- Hetel, L., Daafouz, J., Tarbouriech, S., & Prieur, C. (2013). Stabilization of linear impulsive systems through a nearly-periodic reset. Nonlinear Analysis: Hybrid Systems, 7(1), 4–15.
- Jamiołkowski, A., & Pastuszak, G. (2015). Generalized Shemesh criterion, common invariant subspaces and irreducible completely positive superoperators. Linear and Multilinear Algebra, 63(2), 314–325.
- Khalil, H. (1992). Nonlinear systems. New York, NY: Macmillan.
- King, C., & Nathanson, M. (2006). On the existence of a common quadratic Lyapunov function for a rank one difference. Linear Algebra and its Applications, 419, 400–416.
- Lakshmikantham, V., Bainov, D., & Simeonov, P.S. (1989). Theory of impulsive differential equations. Singapore: World Scientific Pub. Co. Pte. Ltd.
- Liberzon, D. (2003). Switching in systems and control. Boston, MA: Birkhäuser.
- Liberzon, D., Hespanha, J.P., & Morse, A.S. (1999). Stability of switched systems: A Lie-algebraic condition. Systems Control Letters, 37(3), 117–122.
- Liberzon, D., & Morse, A.S. (1999). Basic problems in stability and design of switched systems. IEEE Control Systems, 19, 59–70.
- Lin, H., & Antsaklis, P.J. (2009). Stability and stabilizability of switched linear systems: A survey of recent results. IEEE Transactions on Automatic Control, 54, 308–322.
- Motzkin, T.S., & Taussky, O. (1952). Pairs of matrices with property L. Transactions of the American Mathematical Society, 73, 108–114.
- Narendra, K.S., & Balakrishnan, J. (1994). A common Lyapunov function for stable LTI systems with commuting A-matrices. IEEE Transactions on Automatic Control, 39(4), 2469–2471.
- Santos, E. (2002). Estabilidade em esquemas de controlo comutado (Master’s thesis). Universidade de Aveiro.
- Shemesh, D. (1984). Common eigenvectors of two matrices. Linear Algebra and its Applications, 62, 11–18.
- Shorten, R., Wirth, F., Mason, O., Wulff, K., & King, C. (2007). Stability criteria for switched and hybrid systems. SIAM Review, 49(4), 545–592.
- Shorten, R.N., & Narendra, K.S. (1998). On the stability and existence of common Lyapunov functions for stable linear switching systems. In 37th IEEE Conference on Decision and Control (pp. 3723–3724). IEEE, Tampa, FL.
- Shorten, R.N., & Narendra, K.S. (2002). Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable second order linear time-invariant systems. International Journal of Adaptive Control and Signal Processing, 16, 709–728.
- Sun, Z., & Ge S.S. (2005). Switched linear systems: Control and design. London: Springer-Verlag.
- Yuan, C., & Wu, F. (2015a). Hybrid control for switched linear systems with average dwell time. IEEE Transactions on Automatic Control, 60(1), 240–245.
- Yuan, C., & Wu, F. (2015b). Asynchronous switching output feedback control of discrete-time switched linear systems. International Journal of Control, 8, 1766–1774 Retrieved from http://dx.doi.org/10.1080/00207179.2015.1016454 (Published online 16 Mar 2015).
- Zhao, X., Yin, S., Li, H., & Niu, B. (2015). Switching stabilization for a class of slowly switched systems. IEEE Transactions on Automatic Control, 60(1), 221–226.
- Zhao, X., Zhang, L., Shi, P., & Liu, M. (2012). Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Transactions on Automatic Control, 57(7), 1809–1815.