A robust H_∞-tracking design for uncertain Takagi–Sugeno fuzzy systems with unknown premise variables using descriptor redundancy approach

Abstract

This paper addresses a robust H_∞ fuzzy observer-based tracking design problem for uncertain Takagi–Sugeno fuzzy systems with external disturbances. To have a practical observer-based controller, the premise variables of the system are assumed to be not measurable in general, which leads to a more complex design process. The tracker is synthesised based on a fuzzy Lyapunov function approach and non-parallel distributed compensation (non-PDC) scheme. Using the descriptor redundancy approach, the robust stability conditions are derived in the form of strict linear matrix inequalities (LMIs) even in the presence of uncertainties in the system, input, and output matrices simultaneously. Numerical simulations are provided to show the effectiveness of the proposed method.

Keywords:

• observer-based control
• descriptor redundancy
• uncertain T–S fuzzy system
• unmeasurable premise variables
• H_∞ control
• linear matrix inequality (LMI)

Additional information

Notes on contributors

Mohammad Hassan Asemani

Mohammad Hassan Asemani received his BSc degree in 2006 from the Electrical Engineering Department of the Shiraz University, Shiraz, Iran. He then received his MSc and PhD degrees in control engineering from the Electrical and Computer Engineering Department of Tarbiat Modares University, Tehran, Iran in 2008 and 2012, respectively. He is currently an assistant professor in the Power & Control Department of Shiraz University, Shiraz, Iran. His areas of interest include T–S fuzzy control, control of linear parameter varying (LPV) systems, singularly perturbed systems, observer-based control and linear matrix inequalities in control.

Vahid Johari Majd

Vahid Johari Majd received his BSc degree in 1989 from the Electrical Engineering Department of the University of Tehran, Iran. He then received his MSc and PhD degrees in the area of control theory from the Electrical Engineering Department of the University of Pittsburgh, PA, USA in 1991 and 1995, respectively. He is currently an associate professor in the Control System Department of Tarbiat Modares University, Tehran, Iran, and is the director of Intelligent Control Systems Laboratory. His areas of interest include intelligent identification and control, multi-agent learning, fuzzy control, cooperative control, formation control, robust nonlinear control and fractional order control.