Abstract
In this chapter, we detail different steps to design an interval observer for discrete-time switched linear systems affected by disturbances and measurement noises which are assumed unknown but, bounded with known bounds. The idea is based on the introduction of new matrices to handle the design difficulty of coordinate transformation often used in interval observers synthesis and to provide more design degrees of freedom. The stability conditions of estimation errors are discussed using a common quadratic Lyapunov function and multiple quadratic Lyapunov functions under an average dwell time switching signals. To discuss the effectiveness of the presented methods, a numerical example is given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Efimov, D., Fridman, L., Raïssi, T., Zolghadri, A., Seydou, S.: Interval estimation for LPV systems applying high order sliding mode techniques. Automatica 48, 2365–2371 (2012)
Mitrinovic, D.S.: Analytic Inequalities. Springer, New York (1970). https://doi.org/10.1007/978-3-642-99970-3
Jiang, B., Wang, J.L., Soh, Y.C.: An adaptive technique for robust diagnosis of fault with independent effects on systems outputs. Int. J. Control 75(11), 792–802 (2002)
Dinh, T.N.: Interval observer and Positive observer, Ph.D. Thesis, Université Paris Sud - Paris XI (2014)
Hespanha, J.P., Morse, A.S.: Stability of switched systems with average dwell-time. In: proceedings of the 38th IEEE CDC, pp. 2655–2660. Phoenix, AZ, USA (1999)
Zhu, K., Song, Y., Ding, D., Wei, G., Liu, H.: Robust MPC under event-triggerd mechanism and Round-Robin protocol: an average dwell-time approach. Inf. Sci. 457, 126–140 (2018)
Ethabet, H., Rabehi, D., Efimov, D., Raïssi, T.: Interval estimation for continuous-time switched linear systems. Automatica 90, 230–238 (2018)
Ethabet, H., Raïssi, T., Amairi, M., Aoun, M.: Interval observers design for continuous-time linear switched systems. In: 20th IFAC WC 2017, July 2017. Toulouse, France (2017)
Dinh, T.N., Marouani, G., Raïssi, T., Wang, Z., Messaoud, H.: Optimal interval observers for discrete-time linear switched systems. Int. J. Control 93(11), 2613–2621 (2020)
Marouani, G., Dinh, T.N., Raïssi, T., Messaoud, H.: Interval observers design for discrete-time linear switched systems. In: European Control Conference (ECC), pp. 801–806. IEEEE (2020)
Otsuka, N., Kakehi, D.: Interval switched positive observers for continuous-time switched positive systems under arbitrary switching. IFAC-PapersOnLine 52(11), 250–255 (2019)
Wang, Y.-E., Karimi, H., Wu, D.: Construction of hybrid interval observers for switched linear systems. Inf. Sci. 454–455, 242–254 (2018). July
Wang, Z., Lim, Ch., Shen, Y.: Interval observer design for uncertain discrete time linear systems. Syst. Control Lett. 116, 41–46 (2018). June
Wang, Z., Rodrigues, M., Theilliol, D., Shen, Y.: Actuator fault estimation observer design for discrete-time linear parameter-varying descriptor systems. Int. J. Adapt. Control Signal Process. 29(2), 242–258 (2015)
Raïssi, T., Efimov, D., Zolghadri, A.: Interval state estimation for a class of nonlinear systems. IEEE Trans. Autom. Control 57(1), 260–265 (2011)
Mazenc, F., Bernard, O.: Asymptotically stable interval observers for planar systems with complex poles. IEEE Trans. Autom. Control 55(2), 523–527 (2010). https://doi.org/10.1109/TAC.2009.2037472. Feb.
Gouzé, J.L., Rapaport, A., Hadj-Sadok, M.Z.: Interval observers for uncertain biological systems. Ecol. Model. 133(1–2), 45–56 (2000), ISSN 0304-3800
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Marouani, G., Dinh, T.N., Wang, Z., Raïssi, T., Messaoud, H. (2022). Interval Observers Design for Discrete-Time Linear Switched Systems. In: Shi, P., Stefanovski, J., Kacprzyk, J. (eds) Complex Systems: Spanning Control and Computational Cybernetics: Foundations. Studies in Systems, Decision and Control, vol 414. Springer, Cham. https://doi.org/10.1007/978-3-030-99776-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-030-99776-2_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-99775-5
Online ISBN: 978-3-030-99776-2
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)