Observer-based proportional derivative fuzzy control for singular Takagi-Sugeno fuzzy systems

Abstract

This study investigates the issue of stability analysis and controller synthesis for nonlinear singular systems . Via applying a fuzzy modeling approach, the nonlinear singular system is expressed by a Takagi-Sugeno (T-S) fuzzy model composed of several linear subsystems. Furthermore, the parallel distributed compensation fuzzy controller is designed such that the controlled singular system is stable. Employing Proportional Derivative (PD) control method, the regularity and impulse-free property of the singular systems can be held. However, the PD control method is challengable because the state signals of singular systems are not always measurable. Therefore, a novel fuzzy observer is designed to ensure the existence of estimated states. For the observer-based PD control issue, some sufficient stability conditions are derived for T-S fuzzy singular systems. Moreover, the control gains and observer gains can be conveniently calculated using the Linear Matrix Inequality (LMI) calculation. Finally, two numerical examples are presented to verify the availability and applicability of the proposed design method.