Luenberger observer of impulsive systems: a survey. (English) Zbl 1506.93034
Naifar, Omar (ed.) et al., Advances in observer design and observation for nonlinear systems. Fundamentals and applications. Cham: Springer. Stud. Syst. Decis. Control 410, 71-85 (2022).
Summary: In this chapter, some results on the state estimation of impulsive systems have been conducted. This problem is rarely tackled for this class of systems by researchers and they have designed an observer in the case of autonomous impulsive linear systems. Indeed, only E. A. Medina considered in [Linear impulsive control systems: a geometric approach. Athens, OH: Ohio University (PhD Thesis) (2007)], and E. A. Medina and D. A. Lawrence in [“State estimation for linear impulsive systems”, in: Proceedings of the 2009 American control conference, ACC 2009. Piscataway, NJ: IEEE (2009; doi:10.1109/ACC.2009.5160347)] an observer in the case of autonomous impulsive linear systems, under the condition of strong observability.
For the entire collection see [Zbl 1480.93010].
For the entire collection see [Zbl 1480.93010].
MSC:
| 93B53 | Observers |
| 93C27 | Impulsive control/observation systems |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C05 | Linear systems in control theory |
| 93B07 | Observability |
| 93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |
References:
| [1] | Medina, E.A.: Linear impulsive control systems: a geometric approach. Ph.D. thesis, Ohio University, School of Electrical Engineering and Computer Science (2007) |
| [2] | Medina, E.A., Lawrence, D.A.: State estimation for linear impulsive systems. ACC’09. In: Proceedings of the 2009 Conference on American Control Conference (2009) |
| [3] | Liu, X.: Stability of impulsive control systems with time delay. Math. Comput. Model. 39, 511-519 (2004) · Zbl 1081.93021 |
| [4] | Teel, A.R.: Robust hybrid control systems: an overview of some recent results. In: Lect. Notes Control Inf. Sci. 353, 279-302 (2007) · Zbl 1118.93021 |
| [5] | Yuan, R., Jing, Z., Chen, L.: Uniform asymptotic stability of hybrid dynamical systems with delay. IEEE Trans. Autom. Control 48(2), 344-348 (2003) · Zbl 1364.93694 |
| [6] | Ellouze, I., Vivalda, J.C., Hammami M.A.: A separation principle for linear impulsive systems. Eur J Control, 20, 105-110 (2014) · Zbl 1293.93676 |
| [7] | Gauthier, J.P., Bornard, G.: Observability for any u(t) of a class of nonlinear systems. IEEE Trans. Autom. Control 26(4), 922-926 (1981) · Zbl 0553.93014 |
| [8] | Guan, Z.H., Qian, T.H., Yu, X.: On controllability and observability for a class of impulsive systems. Syst. Control Lett. 47(3), 247-257 (2002) · Zbl 1106.93305 |
| [9] | Medina, E.A., Lawrence, D.A.: Reachability and observability of linear impulsive systems. Automatica 44(5), 1304-1309 (2008) · Zbl 1283.93050 |
| [10] | Xie, G., Wang, L.: Controllability and observability of a class of linear impulsive systems. J. Math. Anal. Appl. 304(1), 36-355 (2005) · Zbl 1108.93022 |
| [11] | Zhaoa, S., Sun, J.: Controllability and observability for a class of time-varying impulsive systems. Nonlinear Anal. Real World Appl. 10(3), 1370-1380 (2009) · Zbl 1159.93315 |
| [12] | Misawa, E.A., Hedrick, J.K.: Nonlinear observers-a state of the art survey. J. Dyn. Syst. Meas. Control 111, 344-352 (1989) · Zbl 0695.93106 |
| [13] | Walcott, B.L., Corless, M.J., Zak, S.K.: Comparative study of nonlinear state obser- vation techniques. Int. J. Control 45(6), 2109-2132 (1987) · Zbl 0627.93012 |
| [14] | Imen Ellouze. Etude de la stabilité et de la stabilisation des systèmes à retard et des systèmes impulsifs. Optimisation et contrôle [math.OC]. Université Paul Verlaine - Metz; Université de Sfax, 2010. Français |
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