Design of state feedback controller for systems with input constrains and actuator faults

This paper presents a method for the controller design of linear systems in the presence of actuator saturation and faults. Firstly, a simple condition is presented, under which any trajectories starting from an ellipsoid Omega₁ will be attracted to zero for linear systems subject to actuator saturation. Then, under this condition, when actuator saturation and actuator faults happen at the same time, the trajectories will remain inside an outer ellipsoid Omega_i, respectively for different mode i. The stability and fault-tolerant ability of the system is measured by the size of these ellipsoids. Based on the above mentioned condition, the problem of estimating the largest constraints is shown to be a optimization problem which can easily be adapted for controller design. An example is given to illustrate the efficiency of the design method.