Diseño de Observadores para Sistemas Híbridos Lineales con Saltos Periódicos (I)

Resumen: En este artículo se proponen observadores híbridos para la estimación del estado en sistemas híbridos lineales con saltos periódicos. Los observadores propuestos poseen una estructura tipo Luenberger y su síntesis está dada en términos de Desigualdades Matriciales Lineales (LMIs, por sus siglas en inglés, Linear Matrix Inequalities) proporcionando un diseño constructivo. La estructura de las LMIs depende de algunas propiedades estructurales de los sistemas híbridos lineales. Ejemplos numéricos ilustran la viabilidad de los métodos propuestos.

¿Cómo citar?

Héctor Ríos & Jorge Dávila. Diseño de Observadores para Sistemas Híbridos Lineales con Saltos Periódicos (I). Memorias del Congreso Nacional de Control Automático, pp. 237-242, 2019.

Palabras clave

Control de Sistemas Lineales, Control de Sistemas No Lineales, Otros Tópicos Afines

• Babaali, M. and Pappas, G.J. (2005). Observability of switched linear systems in continuous time. In M. Morari and L. Thiele (eds.), Hybrid systems: computation and control, Lecture notes in computer science, 103–117. Springer, Berlin.
•  Bainov, D. and Simeonov, P. (1989). Systems with Impulse Effects: Stability, Theory and Applications. Academy Press.
• Bernard, P. and Sanfelice, R. (2018). Observers for hybrid dynamical systems with linear maps and known jump times. In Proc. 57th IEEE Conf. Decision Control, 3140–3145. Miami Beach, FL, USA.
• Branicky, M.S. (1998). Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatatic Control, 43(5), 475–482.
• Carnevale, D., Galeani, S., and Menini, L. (2012). Output regulation for a class of linear hybrid systems. Part 2: stabilization. In Proceedings of the 51st IEEE Conference on Decision and Control, 6157–6162. Maui, Hawaii, USA.
• Carnevale, D., Galeani, S., Menini, L., and Sassano, M. (2016). Hybrid output regulation for linear systems with periodic jumps: Solvability conditions, structural implications and semi-classical solutions. IEEE Transactions on Automatic Control, 61(9), 2416–2431.
• Conte, G., Perdon, A., and Zattoni, E. (2017). Unknown input observers for hybrid linear systems with state jumps. In Proccedings of the 20th IFAC World Congress, volume 50, 6458–6464. Toulouse, France.
• Davila, J., Ríos, H., and Fridman, L. (2012). State observation for nonlinear switched systems using nonhomogeneous high-order sliding mode observers. Asian Journal of Control, 14(4), 911–923.
• Gómez- Gutiérrez, D., Celikovsky, S., Ramírez- Treviño, A., and Castillo-Toledo, B. (2015). On the observer design problem for continuous-time switched linear systems with unknown switchings. Journal of the Franklin Institute, 352(4), 1595 – 1612. doi: https://doi.org/10.1016/j.jfranklin.2015.01.036.
• Goebel, R., Sanfelice, R.G., and Teel, A.R. (2012). Hybrid Dynamical Systems: Modeling, Stability and Robustness. Princeton University Press, New Jersey, USA.
• Kailath, T. (1985). Linear Systems. Prentice-Hall, Upper Saddle River, NJ.
• Lygeros, J., Johansson, K.H., Simi´c, S.N., Zhang, J., and Sastry, S.S. (2003). Dynamical properties of hybrid automata. IEEE Transactions on Automatic Control, 48(1), 2–17.
• Mincarelli, D., Pisano, A., Floquet, T., and Usai, E. (2016). Uniformly convergent sliding mode-based observation for switched linear systems. International Journal of Robust and Nonlinear Control, 26(7), 1549– 1564. doi:10.1002/rnc.3366.
• Possieri, C. and Teel, A.R. (2017). Structural properties of a class of linear hybrid systems and output feedback stabilization. IEEE Transactions on Automatic Control, 62(6), 2704–2719.
• Tanwani, A., Shim, H., and Liberzon, D. (2013). Observability for switched linear systems: Characterization and observer design. IEEE Transactions on Automatic Control, 58(4), 891–904. doi: 10.1109/TAC.2012.2224257.
• Teel, A.R., Forni, F., and Zaccarian, L. (2013). Lyapunovbased sufficient conditions for exponential stability in hybrid systems. IEEE Transactions on Automatic Control, 58(6), 1591–1596. doi:10.1109/TAC.2012.2228039.
• Vidal, R., Chiuso, A., Soatto, S., and Sastry, S. (2003). Observability of linear hybrid systems. In O. Maler and A. Pnueli (eds.), Hybrid systems: computation and control, Lecture notes in computer science, 526–539. Springer, Berlin.
• Zattoni, E., Perdon, A., and Conte, G. (2018). Measurement dynamic feedback output regulation in hybrid linear systems with state jumps. International Journal of Robust and Nonlinear Control, 28(2), 416–436.
• Zavalishchin, S. and Sesekin, A. (1997). Dynamic Impulse Systems. Theory and Applications. Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht.