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2.12 Notes and References
Cheng DZ, Chen HF. Accessibility of switched linear systems. In: Proc 42nd IEEE CDC 2003; 5759–5764.
Dayawansa WP, Martin CF. A converse Lyapunov theorem for a class of dynamical systems which undergo switching. IEEE Trans Automat Contr 1999; 44(4): 751–760.
Dion J-M, Commault C, Van Der Woude J. Generic properties and control of linear structured systems: a survey. Automatica 2003; 39(7): 1125–1144.
Drager LD, Foote RL, Martin CF, Wolfer J. Controllability of linear systems, differential geometry curves in Grassmannians and generalized Grassmannians, and Riccati equations. Acta Applicandae Mathematicae 1989; 16(3): 281–317.
Ezzine J, Haddad AH. Error bounds in the averaging of hybrid systems. IEEE Trans Automat Contr 1989; 34(11): 1188–1192.
Fryszkowski A, Rzezuchowski T. Continuous version of Filippov-Wazewski relaxation theorem. J Diff Equat 1991; 94(2): 254–265.
Gantmacher FR. The Theory of Matrices. New York: Chelsea, 1959.
Ge SS, Sun Z, Lee TH. Reachability and controllability of switched linear discrete-time systems. IEEE Trans Automat Contr 2001; 46(9): 1437–1441.
Gurvits L. Stabilities and controllabilities of switched systems (with applications to the quantum systems). In: Proc 15th Int Symp Math Theory Network Syst 2002.
Hahn W. Stability of Motion. Berlin: Springer-Verlag, 1967.
Harary F. Graph Theory. Reading: Addison-Wesley, 1969.
Horn RO, Johnson CR. Matrix Analysis. New York: Combridge University Press, 1985.
Ingalls B, Sontag ED, Wang Y. An infinite-time relaxation theorem for differential inclusions. Proc Amer Math Soc 2003; 131: 487–499.
Isidori A. Nonlinear Control Systems (3rd ed.). London: Springer-Verlag, 1995.
Kaplan W. Introduction to Analytic Functions. Reading: Addison-Wesley, 1966.
Lin Y, Sontag ED, Wang Y. A smooth converse Lyapunov theorem for robust stability. SIAM J Contr Optimiz 1996; 34(1): 124–160.
Linz P. An Introduction to Formal Languages and Automata (3rd ed.). Sudbury: Jones and Bartlett, 2001.
Smirnov GV. Introduction to the Theory of Differential Inclusions. Providence: AMS, 2002.
Sun Z, Ge SS, Lee TH. Reachability and controllability criteria for switched linear systems. Automatica 2002; 38(5): 775–786.
Tokarzewski J. Stability of periodically switched linear systems and the switching frequency. Int J Syst Sci 1987; 18(4): 697–726.
Vidyasagar M. Nonlinear Systems Analysis (2nd ed.). Eaglewood Cliffs: Prentice Hall, 1993.
Wonham WM. Linear Multivariable Control — A Geometric Approach. Berlin: Spinger-Verlag, 1979.
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(2005). Mathematical Preliminaries. In: Switched Linear Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/1-84628-131-8_2
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DOI: https://doi.org/10.1007/1-84628-131-8_2
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