Reliable observer-based control against sensor failures for fractional order systems

In the paper, the state and sensor failure observer for fractional order systems with order 0 < a < 1 and 1 < a < 2 is proposed to estimate the system state and sensor failures at the same time. In general, unbounded sensor faults will inevitably lead to system failures. Therefore, it is very necessary to study the reliable controller for fractional order systems against sensor failures. Applying the linear matrix inequality concept and the augmented system method, the sensor faults can be in any form, even unbounded. A reliable observer-based controller based on the state and sensor failures estimation is proposed, which can make the system work well regardless of whether the sensor failures. When a = 1, methods proposed in the paper are equivalent to these of the integer order systems, scilicet, our methods can be extended to integer order systems. Finally, a simulation example is used to demonstrate the efficiency of the present methods.