Non-monotonic robust H₂ fuzzy observer-based control for discrete time nonlinear systems with parametric uncertainties

Abstract

A non-monotonic Lyapunov function (NMLF) is deployed to design a robust H₂ fuzzy observer-based control problem for discrete-time nonlinear systems in the presence of parametric uncertainties. The uncertain nonlinear system is presented as a Takagi and Sugeno (T–S) fuzzy model with norm-bounded uncertainties. The states of the fuzzy system are estimated by a fuzzy observer and the control design is established based on a parallel distributed compensation scheme. In order to derive a sufficient condition to establish the global asymptotic stability of the proposed closed-loop fuzzy system, an NMLF is adopted and an upper bound on the quadratic cost function is provided. The existence of a robust H₂ fuzzy observer-based controller is expressed as a sufficient condition in the form of linear matrix inequalities (LMIs) and a sub-optimal fuzzy observer-based controller in the sense of cost bound minimization is obtained by utilising the aforementioned LMI optimisation techniques. Finally, the effectiveness of the proposed scheme is shown through an example.

Keywords:

• non-monotonic Lyapunov function
• parametric uncertainty
• fuzzy control
• robust H₂ control
• discrete-time nonlinear systems
• linear matrix inequality (LMI)
• state observer

Acknowledgements

The authors would like to thank the reviewers for their constructive comments that enhanced the quality of this paper. They would also like to thank APAC research group for their valuable support.

Additional information

Notes on contributors

Siavash Fakhimi Derakhshan

Alireza Fatehi received the BS degree from Isfahan University of Technology, in 1990, the MS degree from Tehran University, Tehran, Iran, in 1995, and Ph.D. degree from Tohoku University, Sendai, Japan, in 2001, all in electrical engineering. Fatehi is currently an associate professor of electrical engineering in K.N. Toosi University of Technology (KNTU), Tehran, Iran. He is director of Advance Process Automation & Control (APAC) research group and a member of Industrial Control Center of Excellence in KNTU. His research interests include industrial control systems, process control systems, intelligent control, multiple model control, nonlinear predictive control, nonlinear identification, and fault detection.

Alireza Fatehi

Siavash Fakhimi Derakhshan received the BS degree in electrical engineering from Sharif University of Technology, Tehran, Iran, in 2003, and the MS and Ph.D. degree in electrical engineering from K.N. Toosi University of Technology, Tehran, Iran, in 2005 and 2012, respectively. His current research interests include nonlinear control, stability analysis in fuzzy systems, fuzzy model-based control, multiple model control, nonlinear predictive control and robust control and filtering.