Robust fuzzy observer‐based fault‐tolerant control: A homogeneous polynomial Lyapunov function approach
Farzaneh Sabbaghian‐Bidgoli, Mohammad Farrokhi
Abstract
Abstract In this paper, a homogeneous polynomial Lyapunov function (HPLF) is employed in robust observer‐based Integrated Fault‐Tolerant Control (IFTC) of nonlinear systems modelled by the polynomial fuzzy model (PFM). This makes the design problem benefit from the conservative reduction property of polynomial Lyapunov functions (PLFs) and simultaneously avoid the emergence of non‐convex terms due to differentiation of the polynomial Lyapunov matrix. As a result, the less conservative sum of square (SOS) conditions are obtained in the form of polynomial matrix inequalities (PMI), which are solved via SOSTOOLS. For the first time, a non‐quadratic Lyapunov function is used to design a polynomial fuzzy unknown‐input observer that estimates the system's states and actuator faults in the presence of model uncertainties and external disturbances. The effectiveness of the proposed approach in providing more relaxed and less conservative results along with the better fault tolerance is illustrated through three simulating examples and compared with the quadratic Lyapunov function (QLF) approach.