H \(\infty \) observer-based sliding mode control for singularly perturbed systems with input nonlinearity
This paper considers the problem of \(H \infty \) observer-based sliding mode control for singularly perturbed systems with input nonlinearities. First, a proper observer is designed such that the observer error system with disturbance attenuation level is asymptotically stable. Then, an observer-based sliding surface is constructed under which a criterion for the input-to-state stability (ISS) of the sliding mode dynamics with respect to the observer error is obtained via linear matrix inequality. The criterion presented is independent of the small parameter, and the upper bound for ISS can be obtained efficiently. In addition, a sliding mode control law is synthesized to guarantee the reachability of the sliding surface in the state estimation space. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed theoretical results.
KeywordsSingularly perturbed systems Linear matrix inequality (LMI) Sliding mode control (SMC) Input-to-state stability (ISS)
This paper is supported by the National Natural Science Foundation of China (11171113, 11471118), the Research Foundation of the Henan Higher Education Institutions of China (16A110006) and the Science and Technology Planning Project of Henan Province of China (162102310619).
- 8.Levant, A.: Transient adjustment of high-order sliding modes. In: Proceedings of the 8th international workshop on variable structure systems, pp. 1–6. Spain (2004)Google Scholar
- 11.Bandyopadhyay, B., Deepak, F., Park, Y.J.: A robust algorithm against actuator saturation using integral sliding mode and composite nonlinear feedback. In: Proceedings of the 17th World Congress the International Federation of Automatic Control Seoul, Korea, pp. 14174–14179 (2008)Google Scholar
- 15.Kokotovic, P.V., Khalil, H.K., O’Reilly, J.: Singular Perturbation Methods in Control: Analysis and Design. Academic Press, London (1986)Google Scholar
- 20.Wang, Z.M., Liu, W., Dai, H.H. Naidu, D.S.: Robust stabilization of model-based uncertain singularly perturbed systems with networked time-delay. In: Proceedings of the 48th IEEE conference on decision and control conference, Shanghai, P.R. China, pp. 7917–7922 (2009)Google Scholar
- 24.Liu, H.P., Sun, F.C., Sun, Z.Q.: Stability analysis and synthesis of fuzzy singularly perturbed systems. IEEE Trans. Fuzzy Syst. 13, 273–284 (2005)Google Scholar
- 25.Moraal, P.E., Grizzle, J.W.: Observer design for nonlinear systems with discrete-time measurements. IEEE Trans. Autom. Control 40, 396–404 (1995)Google Scholar
- 29.Jiang, Z.P., Hill, D.J., Guo, Y.: Semiglobal output feedback stabilization for the nonlinear benchmark example. In: Proceedings of the European Control Conference, Brussels, Belgium (1997)Google Scholar
- 30.Liberzon, D.: Observer-based quantized output feedback control of nonlinear systems. In: Proceedings of the 17th IFAC World Congress, pp. 8039–8043 (2008)Google Scholar
- 31.Wang, Z.M., Liu, W.: Output feedback networked control of singular perturbation. In: Proceedings of the 8th World Congress on Intelligent Control and Automation, Taipei, Taiwan, pp. 645–650 (2011)Google Scholar