Output Feedback Nonlinear General Integral Control

This paper proposes an output feedback nonlinear general integral controller for a class of uncertain nonlinear system. By solving Lyapunov equation, we demonstrate a new proposition on Equal ratio gain technique. By using Equal ratio gain technique, Singular perturbation technique and Lyapunov method, theorem to ensure regionally as well as semi-globally exponential stability is established in terms of some bounded information. Moreover, a real time method to evaluate the ratio coefficients of controller and observer are proposed such that their values can be chosen moderately. Theoretical analysis and simulation results show that not only output feedback nonlinear general integral control has the striking robustness but also the organic combination of Equal ratio gain technique and Singular perturbation technique constitutes a powerful tool to solve the output feedback control design problem of dynamics with the nonlinear and uncertain actions.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Liu, B. (2015) Output Feedback Nonlinear General Integral Control. International Journal of Modern Nonlinear Theory and Application, 4, 101-116. doi: 10.4236/ijmnta.2015.42007.

 [1] Khalil, H.K. (2007) Nonlinear Systems. 3rd Edition, Electronics Industry Publishing, Beijing, pp. 551, 449-453. [2] Liu, B.S. and Tian, B.L. (2012) General Integral Control Design Based on Linear System Theory. Proceedings of the 3rd International Conference on Mechanic Automation and Control Engineering, Vol. 5, 3174-3177. [3] Liu, B.S. and Tian, B.L. (2012) General Integral Control Design Based on Sliding Mode Technique. Proceedings of the 3rd International Conference on Mechanic Automation and Control Engineering, Vol.5, 3178-3181. [4] Liu, B.S., Li, J.H. and Luo, X.Q. (2014) General Integral Control Design via Feedback Linearization. Intelligent Control and Automation, 5, 19-23. http://dx.doi.org/10.4236/ica.2014.51003 [5] Liu, B.S., Luo, X.Q. and Li, J.H. (2014) General Integral Control Design via Singular Perturbation Technique. International Journal of Modern Nonlinear Theory and Application, 3, 173-181. http://dx.doi.org/10.4236/ijmnta.2014.34019 [6] Liu, B.S., Luo, X.Q. and Li, J.H. (2013) General Concave Integral Control. Intelligent Control and Automation, 4, 356-361. http://dx.doi.org/10.4236/ica.2013.44042 [7] Liu, B.S., Luo, X.Q. and Li, J.H. (2014) General Convex Integral Control. International Journal of Automation and Computing, 11, 565-570. http://dx.doi.org/10.1007/s11633-014-0813-6 [8] Liu, B.S. (2014) Constructive General Bounded Integral Control. Intelligent Control and Automation, 5, 146-155. http://dx.doi.org/10.4236/ica.2014.53017 [9] Liu, B.S. (2014) On the Generalization of Integrator and Integral Control Action. International Journal of Modern Nonlinear Theory and Application, 3, 44-52. http://dx.doi.org/10.4236/ijmnta.2014.32007 [10] Liu, B.S. (2015) Equal Ratio Gain Technique and Its Application in Linear General Integral Control. International Journal of Modern Nonlinear Theory and Application, 4, 21-36. http://dx.doi.org/10.4236/ijmnta.2015.41003 [11] Liu, B.S. (2014) Nonlinear General Integral Control Design via Equal Ratio Gain Technique. International Journal of Modern Nonlinear Theory and Application, 3, 256-266. http://dx.doi.org/10.4236/ijmnta.2014.35028 [12] Liu, B.S., Luo, X.Q. and Li, J.H. (2014) Conventional and Added-Order Proportional Nonlinear Integral Observers. International Journal of Modern Nonlinear Theory and Application, 3, 210-220. http://dx.doi.org/10.4236/ijmnta.2014.35023 [13] Gajic, Z. (1995) Lyapunov Matrix Equation in System Stability and Control. Mathematics in Science and Engineering, 195, 30-31.