Stability analysis and stabilization for singular linear systems subject to actuator saturation

This paper investigates the problems of stability analysis and stabilization for singular linear systems subject to actuator saturation. A set invariance condition is derived to ensure that the closed-loop system is regionally regular and impulsive-free and an ellipsoid is contractively invariant. Using this set invariance condition, the estimation of the domain of attraction for a given feedback gain can be formulated as an optimization problem. By viewing the feedback gains as extra free parameters, the optimization problem can be used to design the feedback gain resulting in the largest contractively invariant ellipsoid.