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The problem of robust fault tolerant control for continuous-time fractional-order (FO) systems with interval parameters and sensor faults of

Fault tolerant control research and their application to a wide range of industrial and commercial processes have been the subjects of intensive investigations over the past two decades [

Recently, for the FO controller design problem, many authors have done some valuable works [

This paper investigates the observer-based FO output feedback controller design for the FO systems with interval parameters and sensor faults, the purpose is to design the observer-based FO output feedback control law such that the resulting closed-loop FO system is stable for the order

In this paper, we adopt the following Caputo definition for fractional derivative, which allows utilization of initial values of classical integer-order derivatives with known physical interpretations [

Considering the following fractional-order (FO) LTI systems with interval parameters:

To deal with the uncertain interval, we introduce the following notations:

Let

To investigate the fault tolerant control problem in the event of sensor failures, the fault model should be established first.

Letting sensor faults function matrix as [

Now, introducing the following matrices

Define the observer error as

Combining (

In this section, we give a solution to the stability analysis and the observer-based fractional-order (FO) output feedback control problems formulated in the previous part. We first give the following results which will be used in the proof of our main results.

Let

Let

For any matrices

Now, we are in a position to present a solution to the stability analysis and observer-based FO output feedback control problem.

First, we will present a solution to the stability analysis for FO systems (

Given the controller gain matrix

The FO-LTI interval system (

The observer-based FO output feedback control problem for FO systems (

Given positive scalar constants

The FO-LTI system (

In this subsection, first we will present a solution to the stability analysis for FO systems (

Given the controller gain matrix

Suppose that (

The observer-based FO output feedback control problem for FO systems (

Given positive scalar constants

The FO-LTI system (

Consider the fault tolerant control problem for the fractional-order (FO) systems (

State response

State response

Control input

Control input

State response

State response

Control input

Control input

From these simulation results, it can be seen that the designed observer-based FO output feedback controller ensures the asymptotic stability of the FO systems of

The problem of fault tolerant control for fractional-order (FO) systems with uncertain interval parameters and sensor faults is studied. By establishing sensor fault model and state observer, an observer-based FO output feedback controller, which stabilizes the FO systems of

This work was supported by the National Natural Science Foundation of China (no. 61203047) and the Youth Science Foundation of Henan University of Science and Technology (no. 2012QN006).