Linear optimal fault-tolerant attraction domain for second-order saturating linear system

The assessment of the attraction domain is studied for the second-order saturating linear system with possible faults of the control actuators. The attraction domain is endowed with the property of fault-tolerance by defining the fault-tolerant attraction domain properly which is approached by the ellipse. To ensure the desired convergence speed of the fault-tolerant attraction domain, the poles of the closed-loop system are placed in the circle area of the complex plane by state feedback. Based on the parameter space, the feedback gain space described in the form of the inequality is obtained with respect to the circle pole assignment domain. Under the constraints of the feedback gain space and the amplitude limitation of the control actuators, an optimization problem about the fault-tolerant attraction domain is constructed by the scaling of the reference set, and a method is presented to solve it. Finally, an example shows the effectiveness of the method.